on the equivalence problem of compositions of morphisms and inverse morphisms on it is shown that the equivalence problem of h 1h on the family of context free languages is decidable where h is the family of morphisms and h 1 is the family of inverse morphisms

edge distribution method for solving elliptic boundary value problems with boundary singularities elliptic boundary value problems are difficult to treat in the vicinity of singularities i e edges and corners of the boundary the concentration of electrical charge on the edges and corners of a conductor is perhaps the simplest example of such problems here we provide a rapid method for accurate treatment of these problems it utilizes a green s function based implementation of last passage monte carlo diffusion methods this is combined with a diffusion algorithm for the scaling of solutions to the laplace equation near a corner singularity to yield the solution of a benchmark problem the charge distribution near the edge and corner of a conducting cube

noisy classical field theories with two coupled fields dependence of escape rates on relative field stiffness exit times for stochastic ginzburg landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined the potential in which the fields deterministically evolve and the relative stiffness of the fields themselves the latter is of particular importance in that physical applications will generally require different relative stiffnesses but the effect of varying field stiffnesses has not heretofore been studied in this paper we explore the complete phase diagram of escape times as they depend on the various problem parameters in addition to finding a transition in escape rates as the relative stiffness varies we also observe a critical slowing down of the string method algorithm as criticality is approached

discrete boundary finite element schemes for an exterior problem for the time harmonic maxwell s equation abstract a general boundary integral formulation using galerkin procedure is applied to compute the scattering electric field produced by the diffraction of an incident electromagnetic wave by a perfectly conducting obstacle this electric field satisfies the three dimensional time harmonic maxwell s equations for which the skin currents and charges are to be approximated using boundary finite element method with the help of linear and quadratic finite elements of lagrange type we introduce an approximate surface on which the discrete formulation is defined and construct approximate surface currents and charges in addition we study the existence and the uniqueness of the solution of the discrete problem and develop some error estimates for the currents and charges numerical results are also presented in order to validate our numerical approach

domain decomposition algorithms for indefinite hypersingular integral equations the h and p versions iterative methods for linear systems of algebraic equations arising from the h and p version boundary element discretizations of indefinite strongly elliptic integral equations are considered the integral operators under consideration are strongly singular and therefore are pseudodifferential operators of order plus 1 here we extend the approach introduced by cai and widlund siam j sci statist comput 13 1992 pp 243 258 for finite element discretizations to boundary element discretizations we present an additive schwarz method which is an efficient preconditioner for the gmres an iterative method of conjugate gradient type the rate of convergence of the preconditioned gmres algorithm is shown to be bounded for the h version and grow as log2 p for the p version

on a fem bem formulation for an exterior quasilinear problem in the plane we use a version of the fem bem method introduced by costabel boundary elements ix vol 1 c a brebbia et al eds springer verlag 1987 and han j comput math 8 1990 pp 223 232 to discretize an exterior quasilinear problem we provide error estimates for the galerkin method and propose a fully discrete scheme based on simple quadrature formulas furthermore we show that these numerical integration schemes preserve the optimal rates of convergence finally we present results of numerical experiments involving our discretization method

the h p version of the boundary element method for transmission problems with piecewise analytic data this paper analyzes the rate of convergence of the h p version of the boundary element galerkin method for transmission problems with piecewise analytic data based on the regularity of solutions of integral equations in terms of countably nonmed spaces we design the geometric mesh on the interface gamma and the boundary element subspace containing piecewise polynomials with varying degrees we prove that the boundary element galerkin solution converges exponentially fast to the solution of the integral equation in the h 1 2 gamma times h 1 2 gamma norm

a wavelets method for plane elasticity problem a neumann boundary value problem of plane elasticity problem in the exterior circular domain is reduced into an equivalent natural boundary integral equation and a poisson integral formula with the dtn method using the trigonometric wavelets and galerkin method we obtain a fast numerical method for the natural boundary integral equation which has an unique solution in the quotient space we decompose the stiffness matrix in our numerical method into four circulant and symmetrical or antisymmetrical submatrices and hence the solution of the associated linear algebraic system can be solved with the fast fourier transform fft and the inverse fast fourier transform ifft instead of the inverse matrix examples are given for demonstrating our method has good accuracy of our method even though the exact solution is almost singular

on the dirichlet problem in elasticity for a domain exterior to an arc abstract we consider here a dirichlet problem for the two dimensional linear elasticity equations in the domain exterior to an open arc in the plane it is shown that the problem can be reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc existence uniqueness as well as regularity results for the solution to the boundary integral equations are established in appropriate sobolev spaces in particular asymptotic expansions concerning the singular behavior for the solution near the tips of the arc are obtained by adding special singular elements to the regular splines as test and trial functions an augmented galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi optimal rate of convergence for the approximate solutions

the ehrenfeucht conjecture a compactness claim for finitely generated free monoids abstract we survey recent results on the so called ehrenfeucht conjecture which states for each language l over a finite alphabet there exists a finite subset f of l such that for each pair g h of morphisms on the equation g x h x holds for all x in l if and only if holds for all x in f we point out that the conjecture is closely related to the theory of equations in free monoids we also state a suprising consequence of the conjecture if it holds even noneffectively for all dol languages then the hdol sequence equivalence problem is decidable furthermore we give examples of when the conjecture is known to hold in particular we establish it for all binary languages as well as for all languages when attention is restricted to bounded delay morphisms of some fixed delay

least squares methods for the coupling of fem and bem in the present paper we propose least squares formulations for the numerical solution of exterior boundary value problems the partial differential equation is a first order system in a bounded subdomain and the unbounded subdomain is treated by means of boundary integral equations the first order system is derived from a strongly elliptic second order system the analysis of the present least squares formulations is reduced to the analysis of the galerkin method for the coupling of finite element and boundary element methods fem and bem of the second order problem the least squares approach requires no stability condition however it requires the computation of negative as well as of half integer sobolev norms the arising linear systems can be preconditioned to have condition numbers sim 1 the present methods benefit strongly from the use of biorthogonal wavelets on the coupling boundary and the computation of corresponding equivalent norms in sobolev spaces in particular the application of green s formula leads to an efficient discretization of least squares formulations

critical behavior of the kramers escape rate in asymmetric classical field theories we introduce an asymmetric classical ginzburg landau model in a bounded interval and study its dynamical behavior when perturbed by weak spatiotemporal noise the kramers escape rate from a locally stable state is computed as a function of the interval length an asymptotically sharp second order phase transition in activation behavior with corresponding critical behavior of the rate prefactor occurs at a critical length l c similar to what is observed in symmetric models the weak noise exit time asymptotics to both leading and subdominant orders are analyzed at all interval lengthscales the divergence of the prefactor as the critical length is approached is discussed in terms of a crossover from non arrhenius to arrhenius behavior as noise intensity decreases more general models without symmetry are observed to display similar behavior suggesting that the presence of a phase transition in escape behavior is a robust and widespread phenomenon

a least squares coupling method with finite elements and boundary elements for transmission problems we analyze a least squares formulation for the numerical solution of second order lineartransmission problems in two and three dimensions which allow jumps on the interface in a bounded domain the second order partial differential equation is rewritten as a first order system the part of the transmission problem which corresponds to the unbounded exterior domain is reformulated by means of boundary integral equations on the interface the least squares functional is given in terms of sobolev norms of order 1 and of order 1 2 these norms are computed by approximating the corresponding inner products using multilevel preconditioners for a second order elliptic problem in a bounded domain and for the weakly singular integral operator of the single layer potential on its boundary email protected as preconditioners we use both multigrid and bpx algorithms and the preconditioned system has bounded or mildly growing condition number numerical experiments confirm our theoretical results

spline collocation for a boundary integral equation on polygons with cuts in this paper we construct collocation methods for a modified integral equation of the second kind on the boundary of a polygon with a finite number of cuts cuts are often met in practice and are not treated by the classical methods the double layer potential which degenerates in this situation is modified by the addition of two kinds of terms on each cut they take into account the highly singular functions generated by the cut and lead to a bijective boundary operator this operator remains bijective between spaces of sobolev types with high orders of regularity this allows the construction of collocation methods with quasi optimal estimates and high order of convergence with respect to strong norms they use smoothest splines of odd degree numerical examples of the methods are presented

existence results for a nonlinear transmission problem abstract let o and i be open bounded regular subsets of r n such that the closure of i is contained in o let f o be a regular function on o and let f and g be continuous functions from i r to r by exploiting an argument based on potential theory and on the leray schauder principle we show that under suitable and completely explicit conditions on f and g there exists at least one pair of continuous functions u o u i such that u o 0 in o cl i u i 0 in i u o x f o x for all x o u o x f x u i x for all x i i u o x i u i x g x u i x for all x i where the last equality is attained in certain weak sense a simple example shows that such a pair of functions u o u i is in general neither unique nor locally unique if instead the fourth condition of the problem is obtained by a small nonlinear perturbation of a homogeneous linear condition then we prove the existence of at least one classical solution which is in addition locally unique

coupling of mixed finite elements and boundary elements for a hyperelastic interface problem we apply the coupling of mixed finite elements and boundary integral methods using two integral equations on the coupling boundary to study the weak solvability of a nonlinear elliptic problem arising in elastostatics our procedure is based on both the usual brezzi s theory for linear constrained variational problems and some fundamental tools from nonlinear functional analysis we derive existence and uniqueness of solution for the continuous variational formulations and provide general approximation results for the corresponding galerkin schemes although we consider bounded domains the same analysis applies for the case in which the boundary element region is unbounded

the h p boundary element method for solving 2 and 3 dimensional problems abstract in this survey paper we report on recent developments of the hp version of the boundary element method we consider weakly singular and hypersingular integral equations on polygons and polyhedral surfaces we show that the galerkin solutions computed with the hp version on geometric meshes converge exponentially fast towards the exact solutions of the integral equations the implementation of the hp version of the boundary element method is discussed and adaptive algorithms are given model problems for the coupling of finite elements and boundary elements are also considered numerical results are presented which underline the theoretical results

integration of singular galerkin type boundary element integrals for 3d elasticity problems a galerkin approximation of both strongly and hypersingular boundary integral equation bie is considered for the solution of a mixed boundary value problem in 3d elasticity leading to a symmetric system of linear equations the evaluation of cauchy principal values v p and finite parts p f of double integrals is one of the most difficult parts within the implementation of such boundary element methods bems a new integration method which is strictly derived for the cases of coincident elements as well as edge adjacent and vertex adjacent elements leads to explicitly given regular integrand functions which can be integrated by the standard gauss legendre and gauss jacobi quadrature rules problems of a wide range of integral kernels on curved surfaces can be treated by this integration method we give estimates of the quadrature errors of the singular four dimensional integrals

coupling of finite elements and boundary elements for some nonlinear interface problems abstract this paper considers the symmetric coupling method with boundary elements and finite elements analyzed by costabel and stephan we present experimental rates of convergence for the h version where we achieve the accuracy of the galerkin approximation by refining the mesh in our computations we use as finite elements piecewise bilinear functions and as boundary elements piecewise constant functions

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

coupling of fem and bem in shape optimization in the present paper we consider the numerical solution of shape optimization problems which arise from shape functionals of integral type over a compact region of the unknown shape especially l 2 tracking type functionals the underlying state equation is assumed to satisfy a poisson equation with dirichlet boundary conditions we proof that the shape hessian is not strictly h 1 2 coercive at the optimal domain which implies ill posedness of the optimization problem under consideration since the adjoint state depends directly on the state we propose a coupling of finite element methods fem and boundary element methods bem to realize an efficient first order shape optimization algorithm fem is applied in the compact region while the rest is treated by bem the coupling of fem and bem essentially retains all the structural and computational advantages of treating the free boundary by boundary integral equations

biorthogonal wavelet approximation for the coupling of fem bem we apply multiscale methods to the coupling of finite and boundary element methods to solve an exterior dirichlet boundary value problem for the two dimensional poisson equation adopting biorthogonal wavelet matrix compression to the boundary terms with n degrees of freedom we show that the resulting compression strategy fits the optimal convergence rate of the coupling galerkin methods while the number of nonzero entries in the corresponding stiffness matrices is considerably smaller than n 2

the h p version of the coupling of finite element and boundary element methods for transmission problems in polyhedral domains this paper analyzes the rate of convergence of the h p version of the coupling of the finite element and boundary element method for transmission problems with a linear differential operator with variable coefficients in a bounded polyhedral domain omega 1 and with constant coefficients in the exterior domain omega 2 bbb r 3 backslash overline omega 1 this procedure uses the variational formulation of the differential equation in omega 1 and involves integral operators on the interface between omega 1 and omega 2 the finite elements are used to obtain approximate solutions of the differential equation in omega 1 and the boundary elements are used to obtain approximate solutions of the integral equations for given piecewise analytic data we show that the galerkin solution of this coupling procedure converges exponentially fast in the energy norm if the h p version is used both for finite elements and boundary elements

coupling of finite and boundary element methods for an elastoplastic interface problem a class of transmission problems is considered in which a nonlinear variational problem in one domain is coupled with a linear elliptic problem in a second domain a typical example is a problem from three dimensional elasticity theory where an elastoplastic material is embedded into a linear elastic material the nonlinear problem is given in variational form with a strictly convex functional the linear elliptic problem is described by boundary integral equations on the coupling boundary the typical saddle point structure of such problems is analyzed galerkin approximations are studied which consist of a finite element approximation in the first domain coupled with a boundary element method on the coupling boundary the convergence of the galerkin approximation is based on the saddle point structure which is shown to hold for the exact as well as the discretized problems

multilevel methods for the h p and hp versions of the boundary element method in this paper we give an overview on the definition of finite element spaces for the h p and hp version of the bem along with preconditioners of additive schwarz type we consider screen problems with a hypersingular or a weakly singular integral equation of first kind on an open surface as model problems for the hypersingular integral equation and the h version with piecewise bilinear functions on a coarse and a fine grid we analyze a preconditioner by iterative substructuring based on a non overlapping decomposition of we prove that the condition number of the preconditioned linear system behaves polylogarithmically in h h here h is the size of the subdomains and h is the size of the elements for the hp version and the hypersingular integral equation we comment in detail on an additive schwarz preconditioner which uses piecewise polynomials of high degree on the fine grid and yields also a polylogarithmically growing condition number for the weakly singular integral equation where no continuity of test and trial functions across the element boundaries has to been enforced the method works for nonuniform degree distributions as well numerical results supporting our theory are reported

semi discrete galerkin approximation of the single layer equation by general splines this paper deals with a semi discrete version of the galerkin method for the single layer equation in a plane in which the outer integral is approximated by a quadrature rule a feature of the analysis is that it does not require high precision quadrature or exceptional smoothness of the data instead the assumptions on the quadrature rule are that constant functions are integrated exactly that the rule is based on sufficiently many quadrature points to resolve the approximation space and that the peano constant of the rule is sufficiently small it is then shown that the semi discrete galerkin approximation is well posed for the trial and test spaces we consider quite general piecewise polynomials on quasi uniform meshes ranging from discontinuous piecewise polynomials to smoothest splines since it is not assumed that the quadrature rule integrates products of basis functions exactly one might expect degradation in the rate of convergence to the contrary it is shown that the semi discrete galerkin approximation will converge at the same rate as the corresponding galerkin approximation in the h 0 and h 1 norms

on the adaptive coupling of fem and bem in 2 d elasticity this paper concerns the combination of the finite element method fem and the boundary element method bem using the symmetric coupling as a model problem in two dimensions we consider the hencky material a certain nonlinear elastic material in a bounded domain with navier lame differential equation in the unbounded complementary domain using some boundary integral operators the problem is rewritten such that the galerkin procedure leads to a fem bem coupling and quasi optimally convergent discrete solutions beside this a priori information we derive an a posteriori error estimate which allows up to a constant factor the error control in the energy norm since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh refinement we state adaptive algorithms for the h version of the fem bem coupling illustrating numerical results are included

a fem bem coupling method for a nonlinear transmission problem modelling coulomb friction contact a nonlinear transmission problem modelling elastoplastic interface problems with contact and coulomb friction is reduced to a boundary domain variational inequality we present a corresponding fem bem coupling procedure and derive for its galerkin solution an a priori error estimate furthermore we reformulate the problem as an equivalent saddle point problem whose discretization can be solved by the uzawa algorithm convergence of the fem bem coupling method is proved and numerical results are given

the validity of johnson nedelec s bem fem coupling on polygonal interfaces in this short article we prove that the classical one equation or johnson nedelec coupling of finite and boundary elements can be applied with a lipschitz coupling interface because of the way it was originally approached from the analytical standpoint this bem fem scheme has generally required smooth boundaries and hence produced a consistency error in the finite element part with a variational argument we prove that this requirement is not needed and that stability holds for all pairs of discrete space as it inherits the underlying ellipticity of the problem

on the convergence of the p version of the boundary element galerkin method abstract the authors consider various physical problems which may be formulated in terms of integral equations of the first kind including the two dimensional screen neumann and dirichlet problems in acoustics and crack problems in elasticity sharp regularity results for the solutions are available for these problems proven is the convergence of the p version for some galerkin boundary element schemes based on the integral equation formulations it is shown that the rate of convergence obtained by our method is twice that for the usual h version

variational formulations of transmission problems via fem bem and dtn mappings the purpose of this work is to review some of the main results on the weak solvability and galerkin approximations of interior and exterior transmission problems arising in potential theory and elastostatics both linear and nonlinear model problems are included in our presentation we consider variational formulations based on the combination of mixed finite elements with either boundary integral equations or dirichlet to neumann dtn mappings we provide existence and uniqueness of solution for the continuous formulations and give general approximation estimates for the associated galerkin schemes some open questions are also mentioned

the coupling of boundary integral and finite element methods for the exterior steady oseen problem abstract in this article we present a new numerical method for solving the steady oseen equations in an unbounded plane domain the technique consists in coupling the boundary integral and the finite element methods an artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior homogeneous one the solution in exterior region is represented by an integral equation over the artificial boundary this integral equation is incorporated into a velocity pressure formulation for the interior region and a finite element method is used to approximate the resulting variational problem finally the optimal error estimates of the numerical solution are derived computer results will be discussed in a forthcoming paper

a high frequency hp boundary element method for scattering by convex polygons in this paper we propose and analyze a hybrid hp boundary element method for the solution of problems of high frequency acoustic scattering by sound soft convex polygons in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution we demonstrate both theoretically and via numerical examples exponential convergence with respect to the order of the polynomials moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern in which the dependence on the frequency of all constants is explicit importantly these estimates prove that to achieve any desired accuracy in the computation of these quantities it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases in contrast to the at least linear growth required by conventional methods

new implementation techniques for the exterior stokes problem in the plane abstract we present a method to solve numerically two dimensional stokes problems on exterior domains our scheme is based on the fully discrete bem fem formulation proposed in 21 whose main advantage is that only elemental quadratures are used to approximate the weakly singular boundary integrals we show in this article that it is possible to maintain this important property without using curved triangles in the discretization process this modification makes the method easier to implement and the numerical experiments reveal that it still keeps the optimal order of convergence of the original scheme we also introduce in this paper a new iterative method to solve the complicated linear systems of equations that arises from this type of bem fem discretizations

on the h p version of the boundary element method for symm s integral equation on polygons abstract in this paper we present the numerical implementation of and numerical experiments for the galerkin approximation of symm s integral equation using the h p and h p methods numerical results obtained using an adaptive algorithm are also given the theoretical results for these methods are summarized and are compared with the experimental results

a note on the ellipticity of the single layer potential in two dimensional linear elastostatics we prove that the single layer potential operator of planar linear elastostatics is elliptic in h 1 2 2 if the domain is scaled appropriately

computation of mhd equilibrium of tokamak plasma abstract computation of the mhd equilibrium of a tokamak plasma is reviewed as comprehensively as possible the basic equation of this problem is the grad shafranov equation general remarks on this equation and related issues are first summarized with historical survey of the mhd equilibrium solution where some mathematical discussions on the numerical analysis of the problem are also presented distinguishing features of this problem are seen in treatment of the boundary condition and constraining conditions and we describe them in a rather detailed manner in the main part of this review paper we present a concrete description on the numerical procedures of the mhd equilibrium solvers which are classified into two groups that is the real space solvers and the inverse equilibrium solvers we also describe topics on more general equilibrium models that is the equilibrium with steady flow anisotropic equilibria equilibria with specified current sources and equilibrium evolution brief comments on three dimensional equilibrium solvers are also presented as for application of the mhd equilibrium solvers we present only a small part that is beta limit optimization design of external coils analysis of positional instability and analysis of experimentally obtained data from electromagnetic measurement it is concluded that among various kinds of numerical solution methods we can usually find most adequate ones for the present problem

test sets for context free languages and algebraic systems of equations over a free monoid it is shown that for every context free language l there effectively exists a test set f that is a finite subset f of l such that for any pair g h of morphisms g x h x for all x in f implies g x h x for all x in l this result was claimed earlier but a detailed correct proof is given here together with very recent results on systems of equations over a free monoid this result implies that every algebraic system of equations is equivalent to a finite subsystem

on binary equality sets and a solution to the test set conjecture in the binary case abstract k culik ii and j karhumaki rairo inform theor 14 1980 349 369 conjectured that the equality set of two injective morphisms over a binary alphabet is of the form u v for some possibly empty words u and v here we show that such an equality set is always either of the above form or of the form uw v for some words u w and v as an application we give a simple proof for the test set conjecture in the binary case cf k culik ii and a salomaa j comput system sci 20 1980 379 396 in fact we show that a test set can always be chosen to contain no more than three words

fem and bem coupling for a nonlinear transmission problem with signorini contact this paper is concerned with the interface problem consisting of a nonlinear uniformly monotone partial differential equation in some bounded lipschitz domain omega in reals n n 2 or n geq 3 and the laplace equation with some radiation condition in the unbounded exterior domain omega c reals n setminus overline omega the two problems are coupled by transmission conditions and signorini contact conditions on the interface gamma partial omega the exterior part of the interface problem is rewritten in terms of boundary integral operators this leads to a variational inequality with a nonlinear monotone operator by this approach existence and uniqueness of a solution in appropriate sobolev spaces are obtained its approximation is performed by coupling the finite element method fem in omega and the boundary element method bem the latter living on the interface gamma yielding a discrete monotone variational inequality we present an abstract cea type error estimate and derive asymptotic error estimates

high order boundary conditions and finite elements for infinite domains a finite element method for the solution of linear elliptic problems in infinite domains is proposed the two dimensional laplace helmholtz and modified helmholtz equations outside an obstacle and in a semi infinite strip are considered in detail in the proposed method an artificial boundary b is first introduced to make the computational domain finite then the exact nonlocal dirichlet to neumann dtn boundary condition is derived on b this condition is localized and a sequence of local boundary conditions on b of increasing order is obtained the problem in with a localized dtn boundary condition on b is then solved using the finite element method the numerical stability of the scheme is discussed a hierarchy of special conforming finite elements is developed and used in the layer adjacent to b in conjunction with the local high order boundary condition applied on b an error analysis is given for both nonlocal and local boundary conditions numerical experiments are presented to demonstrate the performance of the method

optimal order multigrid methods for solving exterior boundary value problems the coupling of boundary elements and finite elements combines the advantage of boundary elements for treating domains extended to infinity and that of finite elements in treating the nonhomogeneity of equations and the complexity of domains in the case of the laplacian by taking a circle or a sphere as the artificial coupling boundary it is shown that the corresponding boundary integral equation can be solved without any cost and the coupled system is reduced to a simple finite element system two multigrid methods are proposed to solve this finite element linear system both methods are of optimal order and can be used to solve such finite element equations as efficiently as to solve those arising from interior boundary value problems numerical experiments are included to show the efficiency and advantages of the methods an apparent significance of the methods is that the boundary elements appear neither in the discretization nor in the coding

weak solvability of interior transmission problems via mixed finite elements and dirichlet to neumann mappings we study the weak solvability of an interior linear nonlinear transmission problem arising in steady heat transfer and potential theory for the variational formulation we use a dirichlet to neumann mapping on the interface which is obtained from the application of the boundary integral method to the linear domain and we utilize a mixed finite element method in the nonlinear region existence and uniqueness of solution for the continuous formulation are provided and general approximation results for a fully discrete galerkin method are derived in particular a compatibility condition between the mesh sizes involved is deduced in order to conclude the solvability and stability of this galerkin scheme

hybrid fem bem modeling of finite sized photonic crystals for semiconductor laser beams we propose a 2 d finite element boundary element hybrid method for calculating the spatial distribution and frequency response of electromagnetic waves coming from a semiconductor laser when interacting with a finite sized photonic crystal we thus provide a flexible tool for the design of novel optical and microwave devices among other applications in opposition to current methodologies we simultaneously take into account the laser modes the finiteness of the crystal and the unboundedness of the isotropic medium in which the crystal is embedded at the laser output instead of approximating reflected and transmitted beams by plane waves we use the more realistic hermite gauss functions in the isotropic medium we set an artificial boundary encircling the crystal and define exterior and interior domains radiating solutions for the scattered far field over the exterior are derived analytically through a series of hankel polynomials the interior domain is described by a finite element formulation coupled with dirichlet to neumann maps enforcing laser and far field behaviors results and error analyses are provided in view of future improvements copyright 2010 john wiley sons ltd

the approximation of solutions of elliptic boundary value problems via the p version of the finite element method the approximation theory developed in 11 is used to determine the piecewise polynomial approximability of solutions of elliptic problems on polygonal domains in mathbb r 2 and polyhedra in mathbb r 3 from these estimates convergence orders for the p version of the finite element method applied to such problems are readily obtained the critical issue is the approximation of the singularities which occur at the nonsmooth parts of the domain boundaries it is seen that the estimates of 11 involving the weighted sobolev spaces z l s are well suited for treating such singular functions yielding directly the optimal approximation degree up to an arbitrarily small varepsilon numerical results for two problems from two dimensional linear elasticity are also presented the computations show that the predicted order of convergence is achieved even for low values of p moreover in contrast to the usual h version of the finite element method the point at which the p version enters the asym

analysis of problems in elasto plasticity via an adaptive fem bem coupling method abstract the purpose of this paper is to present an adaptive finite element boundary element coupling method for elasto plastic analysis the finite element method is utilized in regions where plastic material behavior is expected to develop whereas substantial parts of the bounded unbounded linear elastic body are approximated using the boundary element method in order to obtain a computationally efficient coupling method considerable attention is devoted to the generation and adaption of the finite element and boundary element discretizations according to the state of computation the proposed method is computationally efficient since it employs smaller finite element regions unlike available coupling approaches the adaptive finite element boundary element coupling method has the potential advantage that it does not demand predefinition and manual localization of the finite element and boundary element sub domains

local error estimates for the galerkin method applied to strongly elliptic integral equations on open curves saranen math comp 48 1987 pp 485 502 proved local estimates in sobolev norms for the galerkin method applied to strongly elliptic equations on smooth closed curves in the plane we extend his results to the case of open curves of particular interest are weakly singular and hypersingular integral equations on a slit an interesting outcome from our result is that we can judge the orders of convergence of the local errors in some norms that do not exist in the global sense

on the asymptotic convergence of collocation methods with spline functions of even degree we investigate the collocation of linear one dimensional strongly elliptic integro dif ferential or more generally pseudo differential equations on closed curves by even degree polynomial splines the equations are collocated at the respective midpoints subject to uniform nodal grids of the even degree s splines we prove quasioptimal and optimal order asymptotic error estimates in a scale of sobolev spaces the results apply in particular to boundary element methods used for numerical computations in engineering applications the equations considered include fredholm integral equations of the second and the first kind singular integral equations involving cauchy kernels and integro differential equations having convolutional or constant coefficient principal parts respectively the error analysis is based on an equivalence between the collocation and certain varia tional methods with different degree splines as trial and as test functions we further need to restrict our operators essentially to pseudo differential operators having convolutional prin cipal part this allows an explicit fourier analysis of our operators as well as of the spline spaces in terms of trigonometric polynomials providing babuska s stability condition based on strong ellipticity our asymptotic error estimates extend partly those obtained by d n arnold and w l wendland from the case of odd degree splines to the case of even degree splines 1 introduction in this paper we investigate the asymptotic convergence of the collocation method using even degree polynomial splines applied to strongly elliptic systems of pseudo differential equations on closed curves with convolutional prin cipal part the collocation here employs the gauss points of one point integration as collocation points which corresponds to the usual boundary element collocation in applications 5 12 17 19 26 31 34 this is in contrast to the method investigated by g schmidt in 29 where one collocates at the break points of even order splines the asymptotic convergence properties for the standard galerkin method with splines of arbitrary orders are well known 22 for the collocation method however asymptotic convergence up to now has been shown for strongly elliptic systems only in the case of odd order splines by d n arnold and w l wendland 7

coupling of finite element and boundary integral methods for electromagnetic scattering in a two layered medium consider a time harmonic electromagnetic plane wave incident on an inhomogeneity embedded in a two layered medium in this paper a method of coupling of finite element and boundary integral equation methods is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases the well posedness of the continuous and discrete problems as well as optimal error estimates for the coupled variational approximations are obtained numerical results are included to illustrate the accuracy with the optimal convergence property of the proposed method and to show the wave features in a two layered medium

on the h adaptive coupling of fe and be for viscoplastic and elasto plastic interface problems this paper presents a posteriori error estimates for the symmetric finite element and boundary element coupling for a nonlinear interface problem a bounded body with a viscoplastic or plastic material behaviour is surrounded by an elastic body the nonlinearity is treated by the finite element method while large parts of the linear elastic body are approximated using the boundary element method based on the a posteriori error estimates we derive an algorithm for the adaptive mesh refinement of the boundary elements and the finite elements its implementation is documented and numerical examples are included

order of phase transitions in barrier crossing a spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied depending on the potential the transition can be first or second order but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier in this paper we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary in both space and time and whose zero noise dynamics are governed by a smooth polynomial potential we show that a quartic potential barrier can have only second order transitions confirming an earlier conjecture d l stein j stat phys 114 1537 2004 we then derive through a combination of analytical and numerical arguments both necessary and sufficient conditions to have a first order vs a second order transition in noise induced activation behavior for a large class of systems with smooth polynomial potentials of arbitrary order we find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier

balance of many valued transductions and equivalence problems the notion of balance of two morphisms on a given language is generalized to deal with the whole family of rational transductions the usefulness of balance for proving decidability of equivalence of rational transductions is established in particular an alternative proof for a result of culik showing the decidability of the equivalence problem of single valued rational transductions on regular languages is given in addition a new result showing the decidability of the equivalence problem of inverses of single valued rational transductions on regular languages is obtained

an adaptive two level method for the coupling of nonlinear fem bem equations in this paper an a posteriori error estimate for nonlinear coupled fem bem equations is derived by using hierarchical basis techniques based on the properties of two level additive schwarz operators for linearized differential equations and weakly singular integral equations easily computable local error indicators are obtained an algorithm for adaptive error control which allows independent refinements of the finite elements and the boundary elements is formulated and numerical results for the linear and nonlinear case are included

on the convergence of collocation methods for boundary integral equations on polygons the integral equations encountered in boundary element methods are frequently solved numerically using collocation with spline trial functions convergence proofs and error estimates for these approximation methods have been only available in the following cases fredholm integral equations of the second kind 4 7 one dimensional pseudodifferential equations and singular integral equations with piecewise smooth coefficients on smooth curves 2 3 17 26 29 and some special results on the classical neumann integral equation of potential theory for polygonal plane domains 5 8 9 here we give convergence proofs for collocation with piecewise linear trial functions for neumann s integral equation and symm s integral equation on plane curves with corners we derive asymptotic error estimates in sobolev norms and analyze the effect of graded meshes 0 introduction in this paper we give convergence proofs and asymptotic error estimates in sobolev norms for collocation with piecewise linear spline trial func tions applied to two basic integral equations of potential theory on plane polygons namely the integral equation of the second kind with the double layer potential neumann s integral equation and the integral equation of the first kind with the simple layer potential symm s integral equation we use an idea of arnold and wendland 2 namely considering dirac delta functions the test functions in the collocation method as second derivatives of piecewise linear functions therefore similar results as presented here should be possible for splines of higher odd order corresponding results for even order splines are not yet available thus for one of the simplest methods of numerically solving dirichlet s problem on a plane domain with corners the midpoint collocation with piecewise constant trial functions for the first kind integral equation with the simple layer potential convergence is still an open problem the method of fourier series that yields the convergence proof in the case of a smooth boundary 27 cannot be applied in the presence of corners we apply the method of local mellin transformation that has previously been used to derive error estimates for galerkin methods for a wide class of operators including those occurring in boundary element methods in acoustics electromag

wavelet least squares methods for boundary value problems this paper is concerned with least squares methods for the numerical solution of operator equations our primary focus is the discussion of the following conceptual issues the selection of appropriate least squares functionals their numerical evaluation in the special light of recent developments of wavelet methods and a natural way of preconditioning the resulting systems of linear equations we describe first a general format of variational problems that are well posed in a certain natural topology in order to illustrate the scope of these problems we identify several special cases such as second order elliptic boundary value problems their formulation as a first order system transmission problems the system of stokes equations or more general saddle point problems particular emphasis is placed on the separate treatment of essential nonhomogeneous boundary conditions we propose a unified treatment based on wavelet expansions in particular we exploit the fact that weighted sequence norms of wavelet coefficients are equivalent to relevant function norms arising in the least squares context this provides access to difficult norms efficient preconditioners and in the case of first order systems optimal l2 error estimates

symmetric coupling of boundary elements and raviart thomas type mixed finite elements in elastostatics both mixed finite element methods and boundary integral methods are important tools in computational mechanics according to a good stress approximation recently even low order mixed methods of raviart thomas type became available for problems in elasticity since either methods are robust for critical poisson ratios it appears natural to couple the two methods as proposed in this paper the symmetric coupling changes the elliptic part of the bilinear form only hence the convergence analysis of mixed finite element methods is applicable to the coupled problem as well specifically we couple boundary elements with a family of mixed elements analyzed by stenberg the locking free implementation is performed via lagrange multipliers numerical examples are included

high order convergence for collocation of second kind boundary integral equations on polygons we propose collocation methods with smoothest splines to solve the integral equation of the second kind on a plane polygon they are based on the bijectivity of the double layer potential between spaces of sobolev type with arbitrary high regularity and involving the singular functions generated by the corners if splines of order 2m 1 are used we get quasi optimal estimates in h m norm and optimal order convergence for the h k norm if 0 le k le m numerical experiments are presented

numerical treatment of vertex singularities and intensity factors for mixed boundary value problems for the laplace equation in r 3 a numerical method for the computation of the singular behavior of the solution of the laplace equation is proposed it is shown that the accuracy of the computed stress intensity factor by the h p and h text p version of the finite element method has the same order as the square of the error of the solution measured in the energy norm numerical examples are given

on test sets for checking morphism equivalence on languages with fair distribution of letters abstract a test set for a language l is a finite subset t of l with the property that each pair of morphisms that agrees on t also agrees on l some results concerning test sets for languages with fair distribution of letters are presented the first result is that every d0l language with fair distribution of letters has a test set the second result shows that every language l with fair distribution has a test set relative to morphisms g h which have bounded balance on l these results are generalizations of results of culik ii and karhumaki 1983

on hp error estimation in the bem for a three dimensional helmholtz exterior problem the purpose of the paper is to give an a priori convergence estimate for the hp adaptive boundary element method the method is used to solve an exterior helmholtz boundary value problem with the robin s boundary condition in the three dimensional space the mathematical model describes an acoustic wave scattering problem on a bounded elastic solid where time harmonic process is assumed the estimate consists of three parts which correspond to influence of three errors caused by interpolation of functions geometry and an incident wave

on the coupling of vem and bem in two and three dimensions this paper introduces and analyzes the combined use of the virtual element method vem and the boundary element method bem to numerically solve linear transmission problems in two and three dime

a priori error estimates for hp penalty bem for contact problems in elasticity the purpose of the paper is to obtain a priori error estimates for the hp version of penalty galerkin bem applied to frictionless contact problems in elasticity the error analysis is divided into two parts at first we consider the error caused by the approximation of the variational inequality or lagrange multiplier formulation with the penalty problem under additional regularity assumptions we derive a linear convergence rate with respect to the penalty parameter then the discretization error between the solution of the penalty problem and its galerkin approximation is considered we show two types of the best approximation property which is similar to the cea s lemma but the estimate depends on the penalty parameter finally we derive an a priori estimate for the error between the exact solution u of the variational inequality and the boundary element galerkin solution of the penalty problem for u h 3 2 c n we obtain the convergence rate o h p 1 when choosing the penalty parameter e c h p 1 for arbitrary fixed 0 1 and c 0

fe be coupling for an acoustic fluid structure interaction problem residual a posteriori error estimates summary in this paper we develop an a posteriori error analysis of a coupling of finite elements and boundary elements for a fluid structure interaction problem in two and three dimensions this problem is governed by the acoustic and the elastodynamic equations in time harmonic vibration our methods combine integral equations for the exterior fluid and finite element methods for the elastic structure it is well known that due to the reduction of the boundary value problem to boundary integral equations the solution is not unique in general however due to superposition of various potentials we consider a boundary integral equation which is uniquely solvable and which avoids the irregular frequencies of the negative laplacian operator of the interior domain in this paper two stable procedures are considered one is based on the non symmetric formulation and the other one is based on a symmetric formulation for both formulations we derive reliable residual a posteriori error estimates from the estimators we compute local error indicators which allow us to develop an adaptive mesh refinement strategy for the two dimensional case we perform an adaptive algorithm on triangles and for the three dimensional case we use hanging nodes on hexahedrons numerical experiments underline our theoretical results copyright c 2000 john wiley sons ltd

on the asymptotic convergence of collocation methods we prove quasioptimal and optimal order estimates in various sobolev norms for the approximation of linear strongly elliptic pseudodifferential equations in one independent variable by the method of nodal collocation by odd degree polynomial splines the analysis pertains in particular to many of the boundary element methods used for numerical computation in engineering applications equations to which the analysis is applied include fredholm integral equations of the second kind certain first kind fredholm equations singular integral equations involving cauchy kernels a variety of integro differential equations and two point boundary value problems for ordinary differential equations the error analysis is based on an equivalence which we establish between the collocation methods and certain nonstandard galerkin methods we compare the collocation method with a standard galerkin method using splines of the same degree showing that the galerkin method is quasioptimal in a sobolev space of lower index and furnishes optimal order approximation for a range of sobolev indices containing and extending below that for the collocation method and so the standard galerkin method achieves higher rates of convergence

on the coupled bem and fem for a nonlinear exterior dirichlet problem in r2 in this paper we apply the coupling of boundary integral and finite element methods to solve a nonlinear exterior dirichlet problem in the plane specifically the boundary value problem consists of a nonlinear second order elliptic equation in divergence form in a bounded inner region and the laplace equation in the corresponding unbounded exterior region in addition to appropriate boundary and transmission conditions the main feature of the coupling method utilized here consists in the reduction of the nonlinear exterior boundary value problem to an equivalent monotone operator equation we provide sufficient conditions for the coefficients of the nonlinear elliptic equation from which existence uniqueness and approximation results are established then we consider the case where the corresponding operator is strongly monotone and lipschitz continuous and derive asymptotic error estimates for a boundary finite element solution we prove the unique solvability of the discrete operator equations and based on a strang type abstract error estimate we show the strong convergence of the approximated solutions moreover under additional regularity assumptions on the solution of the continous operator equation the asymptotic rate of convergenceo h is obtained

a dual dual mixed formulation for nonlinear exterior transmission problems we combine a dual mixed finite element method with a dirichletto neumann mapping derived by the boundary integral equation method to study the solvability and galerkin approximations of a class of exterior nonlinear transmission problems in the plane as a model problem we consider a nonlinear elliptic equation in divergence form coupled with the laplace equation in an unbounded region of the plane our combined approach leads to what we call a dual dual mixed variational formulation since the main operator involved has itself a dual type structure we establish existence and uniqueness of solution for the continuous and discrete formulations and provide the corresponding error analysis by using raviart thomas elements the main tool of our analysis is given by a generalization of the usual babuska brezzi theory to a class of nonlinear variational problems with constraints

the k operator and the galerkin method for strongly elliptic equations on smooth curves local estimates superconvergence in the l2 norm for the galerkin approximation of the integral equation lu f is studied where i is a strongly elliptic pseudodifferential operator on a smooth closed or open curve let uf be the galerkin approximation to u by using the operator an operator that averages the values of uh we will construct a better approximation than uh itself that better approximation is a legacy of the highest order of convergence in negative norms for symm s equation on a slit the same order of convergence can be recovered if the mesh is suitably graded in this paper we shall study a way of increasing the order of local convergence in the l2 norm for the galerkin approximation to the solution of strongly ellip tic pseudodifferential equations on a smooth closed or open curve in r2 this kind of integral equation is of importance in solving interior or exterior bound ary value problems of potential theory the most common example is symm s first kind integral equation with logarithmic kernel see 6 7 12 other appli cations are hypersingular integral equations and singular integral equations of cauchy type which occur e g in elasticity see 18 for general petrov galerkin methods when smoothest splines are used as trial and test functions local error estimates were proved in 11 for smooth closed curves and in 16 for smooth open curves consider for example symm s equation with piecewise constant functions used as trial and test functions it was proved that the local l2 error converges with order 0 h in the case of smooth closed curves 11 and with order 0 hxi2 in the case of smooth open curves 16 however it is well known that the highest orders of global convergence achieved in negative norms are 0 h3 for the closed smooth case 5 and 0 h for the open smooth case 4 13 the purpose of this article is to construct from the galerkin solution a better approximate solution which inherits the highest possible orders of global convergence to give best local con vergence in the l2 norm e g in the example mentioned above order 0 hy for the closed case and 0 h for the open case can be achieved locally in the l2 norm that better approximation is constructed by averaging the values of the galerkin solution using the k operator

reconstruction of the equilibrium of the plasma in a tokamak and identification of the current density profile in real time the reconstruction of the equilibrium of a plasma in a tokamak is a free boundary problem described by the grad shafranov equation in axisymmetric configuration the right hand side of this equation is a nonlinear source which represents the toroidal component of the plasma current density this paper deals with the identification of this nonlinearity source from experimental measurements in real time the proposed method is based on a fixed point algorithm a finite element resolution a reduced basis method and a least square optimization formulation this is implemented in a software called equinox with which several numerical experiments are conducted to explore the identification problem it is shown that the identification of the profile of the averaged current density and of the safety factor as a function of the poloidal flux is very robust

a dual dual formulation for the coupling of mixed fem and bem in hyperelasticity we combine a dual mixed finite element method with the boundary integral equation method to study the solvability and galerkin approximations of a linear nonlinear transmission problem arising in plane elastostatics our approach is based on the introduction of the strain tensor as an auxiliary unknown in the finite element domain and it leads to what we call a dual dual mixed formulation since the corresponding operator equation becomes of a twofold saddle point structure we derive existence and uniqueness of solution for the continuous and discrete formulations and provide the associated error analysis in particular we extend the finite element space for plane elasticity given by the peers element and define an explicit finite element boundary element subspace satisfying all the required compatibility conditions most of our analysis makes use of an extension of the classical babuska brezzi theory to a class of nonlinear saddle point problems

fem bem coupling methods for tokamak plasma axisymmetric free boundary equilibrium computations in unbounded domains abstract incorporating boundary conditions at infinity into simulations on bounded computational domains is a repeatedly occurring problem in scientific computing the combination of finite element methods fem and boundary element methods bem is the obvious instrument and we adapt here for the first time the two standard fem bem coupling approaches to the free boundary equilibrium problem the johnson nedelec coupling and the bielak maccamy coupling we recall also the classical approach for fusion applications dubbed according to its first appearance von hagenow lackner coupling and present the less used alternative introduced by albanese blum and de barbieri in 2 we show that the von hagenow lackner coupling suffers from undesirable non optimal convergence properties that suggest that other coupling schemes in particular johnson nedelec or albanese blum de barbieri are more appropriate for non linear equilibrium problems moreover we show that any of such coupling methods requires newton like iteration schemes for solving the corresponding non linear discrete algebraic systems

duality estimates for the numerical solution of integral equations we formulate and prove aubin nitsche type duality estimates for the error of general projection methods examples of applications include collocation methods and augmented galerkin methods for boundary integral equations on plane domains with corners and three dimensional screen and crack problems for some of these methods we obtain higher order error estimates in negative norms in cases where previous formulations of the duality arguments were not applicable

some boundary element methods using dirac s distributions as trial functions in this article a boundary element method using dirac s distributions as trial functions is proposed as test functions we use smoother splines the computational complexity of this method is comparable with the collocation method and it converges with less regularity requirements on the boundary data asymptotic error analysis is derived an example considering solution of the potential problem is discussed in some detail finally a numerical example demonstrates the applicability of the method in practical calculations

a fully discrete bem fem method for an exterior elasticity system in the plane abstract we present a modified version of the usual bem fem coupling for the exterior elasticity problem in the plane cf costabel and stephan siam j numer anal 27 1990 1212 1226 this new formulation allows us to take advantage of techniques from hsiao et al computing 25 1980 557 566 to compute the boundary integral terms using simple quadrature formulas we provide error estimates for the galerkin method and prove that the corresponding fully discrete scheme preserves the optimal rates of convergence

coupled finite element hierarchical boundary element methods for dynamic soil structure interaction in the frequency domain summary this paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil structure interaction problems in the frequency domain the application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods three coupling methodologies are presented and their computational performance is assessed through numerical examples it is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient as it requires the assembly of a dynamic soil stiffness matrix iterative solution procedures are presented as well and it is shown that the application of such schemes to dynamic soil structure interaction problems in the frequency domain is not trivial as convergence can hardly be achieved if no relaxation procedure is incorporated aitken s 2 method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter while a novel relaxation technique is proposed for parallel iterative algorithms it is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain the fastest convergence is observed if neumann boundary conditions are imposed on the stiffest subdomain the use of a dedicated solver for each subdomain hence results in a reduced computational effort a monolithic coupling strategy often used for the solution of fluid structure interaction problems is also introduced the governing equations are simultaneously solved in this approach while the assembly of a dynamic soil stiffness matrix is avoided copyright 2013 john wiley sons ltd

optimal order collocation for the mixed boundary value problem on polygons in usual boundary elements methods the mixed dirichlet neumann problem in a plane polygonal domain leads to difficulties because of the transition of spaces in which the problem is well posed we build collocation methods based on a mixed single and double layer potential this indirect method is constructed in such a way that strong ellipticity is obtained in high order spaces of sobolev type the boundary values of this potential define a bijective boundary operator if a modified capacity adapted to the problem is not 1 this condition is analogous to the one met in the use of the single layer potential and is not a problem in practical computations the collocation methods use smoothest splines and known singular functions generated by the corners if splines of order 2m 1 are used we get quasi optimal estimates in h m norm the order of convergence is optimal in the sense that it is fixed by the approximation properties of the first missed singular function

the uncoupling of boundary integral and finite element methods for nonlinear boundary value problems abstract in this paper the uncoupling of boundary integral and finite element methods is applied to study the weak solvability of certain nonlinear exterior boundary value problems as a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane which becomes the laplace equation in the corresponding unbounded exterior region we provide sufficient conditions for the nonlinear coefficients from which existence uniqueness and approximation results are established in particular nonlinear equations yielding both monotone and nonmonotone operators are analyzed

coupling regularization and adaptive hp bem for the solution of a delamination problem in this paper we couple regularization techniques with the adaptive hp version of the boundary element method hp bem for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions as a model example we treat the delamination of composite structures with a contaminated interface layer this problem has a weak formulation in terms of a nonsmooth variational inequality the resulting hemivariational inequality is first regularized and then discretized by an adaptive hp bem we give conditions for the uniqueness of the solution and provide an a priori error estimate furthermore we prove the very first a posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation thus enabling hp adaptivity various numerical experiments illustrate the behavior strengths and limitations of the proposed high order approximation scheme