convergence and superconvergence of staggered discontinuous galerkin methods for the three dimensional maxwell s equations on cartesian grids in this paper a new type of staggered discontinuous galerkin methods for the three dimensional maxwell s equations is developed and analyzed the spatial discretization is based on staggered cartesian grids so that many good properties are obtained first of all our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the gauss law moreover the mass matrices are diagonal thus time marching is explicit and is very efficient our method is high order accurate and the optimal order of convergence is rigorously proved it is also very easy to implement due to its cartesian structure and can be regarded as a generalization of the classical yee s scheme as well as the quadrilateral edge finite elements furthermore a superconvergence result that is the convergence rate is one order higher at interpolation nodes is proved numerical results are shown to confirm our theoretical statements and applications to problems in unbounded domains with the use of pml are presented a comparison of our staggered method and non staggered method is carried out and shows that our method has better accuracy and efficiency

analysis of a finite element method for maxwell s equations the use of finite elements to discretize the time dependent maxwell equations on a bounded domain in three dimensional space is analyzed energy norm error estimates are provided when general finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

solving maxwell s equations in singular domains with a nitsche type method in this paper we propose and analyze a method derived from a nitsche approach for handling boundary conditions in the maxwell equations several years ago the nitsche method was introduced to impose weakly essential boundary conditions in the scalar laplace operator then it has been worked out more generally and transferred to continuity conditions we propose here an extension to vector div curl problems this allows us to solve the maxwell equations particularly in domains with reentrant corners where the solution can be singular we formulate the method for both the electric and magnetic fields and report some numerical experiments

convergence of the backward euler method for type ii superconductors abstract our paper is devoted to the study of a nonlinear degenerate transient eddy current problem of the type t e 1 p e e 0 p 1 along with appropriate initial and boundary conditions we design a nonlinear time discrete numerical scheme for the approximation in suitable function spaces we show the well posedness of the problem prove the convergence of the approximation to a weak solution and finally derive the error estimates in the proofs the monotonicity methods and the minty browder argument are employed

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

exact convex relaxation of optimal power flow in radial networks the optimal power flow opf problem determines a network operating point that minimizes a certain objective such as generation cost or power loss it is nonconvex we prove that a global optimum of opf can be obtained by solving a second order cone program under a mild condition after shrinking the opf feasible set slightly for radial power networks the condition can be checked a priori and holds for the ieee 13 34 37 123 bus networks and two real world networks

equivalent relaxations of optimal power flow several convex relaxations of the optimal power flow opf problem have recently been developed using both bus injection models and branch flow models in this paper we prove relations among three convex relaxations a semidefinite relaxation that computes a full matrix a chordal relaxation based on a chordal extension of the network graph and a second order cone relaxation that computes the smallest partial matrix we prove a bijection between the feasible sets of the opf in the bus injection model and the branch flow model establishing the equivalence of these two models and their second order cone relaxations our results imply that for radial networks all these relaxations are equivalent and one should always solve the second order cone relaxation for mesh networks the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second order cone relaxation therefore for mesh networks one should either solve the chordal relaxation or the socp relaxation trading off tightness and the required computational effort simulations are used to illustrate these results

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

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

a general non linear optimization algorithm for lower bound limit analysis the non linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided the algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required as with interior point methods for linear programming the number of iterations is affected only little by the problem size some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non linear yield criteria copyright 2002 john wiley sons ltd

error analysis of finite element methods for 3 d maxwell s equations in dispersive media we consider the time dependent maxwell s equations in dispersive media on a bounded three dimensional domain a semi discrete standard finite element method and a semi discrete mixed finite element method are developed and error estimates are provided we believe this is the first finite element error analysis carried out for maxwell s equations in dispersive media

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

continuous galerkin methods for solving the time dependent maxwell equations in 3d geometries a few years ago costabel and dauge proposed a variational setting which allows one to solve numerically the time harmonic maxwell equations in 3d geometries with the help of a continuous approximation of the electromagnetic field in this paper we investigate how their framework can be adapted to compute the solution to the time dependent maxwell equations in addition we propose some extensions such as the introduction of a mixed variational setting and its discretization to handle the constraint on the divergence of the field 2007 elsevier inc all rights reserved

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

multiscale asymptotic method for maxwell s equations in composite materials in this paper we discuss the multiscale analysis of maxwell s equations in composite materials with a periodic microstructure the new contributions in this paper are the determination of higher order correctors and the explicit convergence rate for the approximate solutions see theorem 2 3 consequently we present the multiscale finite element method and derive the convergence result see theorem 4 1 the numerical results demonstrate that higher order correctors are essential for solving maxwell s equations in composite materials

limit analysis of plates and slabs using a meshless equilibrium formulation a meshless element free galerkin efg equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs in the formulation pure moment fields are approximated using a moving least squares technique which means that the resulting fields are smooth over the entire problem domain there is therefore no need to enforce continuity conditions at interfaces within the problem domain which would be a key part of a comparable finite element formulation the collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems the combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes and stable and accurate solutions can be obtained with minimal computational effort the von mises and nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second order cone constraints ensuring that the resulting optimization problem can be solved using efficient interior point solvers finally the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems

augmented formulations for solving maxwell equations we consider augmented variational formulations for solving the static or time harmonic maxwell equations for that a term is added to the usual h curl conforming formulations it consists of a weighted l2 scalar product between the divergence of the em and the divergence of test fields in this respect the methods we present are h curl div conforming we also build mixed augmented variational formulations with either one or two lagrange multipliers to dualize the equation on the divergence and when applicable the relation on the tangential or normal trace of the field it is proven that one can derive formulations which are equivalent to the original static or time harmonic maxwell equations in the latter case spurious modes are automatically excluded numerical analysis and experiments will be presented in the forthcoming paper augmented formulations for solving maxwell equations numerical analysis and experiments in preparation

application of a gpu accelerated hybrid preconditioned conjugate gradient approach for large 3d problems in computational geomechanics this paper presents a hybrid preconditioning technique for conjugate gradient method and discusses its parallel implementation on graphic processing unit gpu for solving large sparse linear systems arising from application of interior point methods to conic optimization problems in the context of nonlinear finite element limit analysis fela for computational geomechanics for large 3d problems the use of direct solvers in general becomes prohibitively expensive due to exponentially growing memory requirements and computational time besides the so called saddle point systems resulting from use of optimization framework is not an exemption on the other hand although preconditioned iterative methods have moderate storage requirements and therefore can be applied to much larger problems than direct methods they usually exhibit high number of iterations to reach convergence in present paper we show that this problem can be effectively tackled using the proposed hybrid preconditioner along with an elaborate implementation on gpu furthermore numerical results verify the robustness and efficiency of the proposed technique

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

the influence of the linearisation of the yield surface on the load bearing capacity of reinforced concrete slabs this paper will demonstrate that the degree of linearisation of the yield surface has a major impact on the bearing capacity when the lower bound theorem of ideal plasticity for reinforced concrete slabs combined with linear mathematical programming methods are applied the finite element descretization is applied and it is shown that the influence of a refinement of the yield surface linearisation may be more important than the refinement of the geometrical mesh

ellipsoidal load domain shakedown analysis with von mises yield criterion a robust optimization approach summary the static formulation of elastic shakedown analysis based upon melan s lower bound theorem can essentially be viewed as a robust optimization problem this paper discusses an advantage that is enjoyed by taking this perspective specifically we assume the von mises yield criterion and an ellipsoidal load domain in this setting the shakedown analysis problem which is viewed as robust second order cone programming can be recast as semidefinite programming copyright 2016 john wiley sons ltd

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

a singular field method for maxwell s equations numerical aspects for 2d magnetostatics the present paper deals with the solution of maxwell type problems by means of nodal h1 conforming finite elements in a nonconvex piecewise regular domain surrounded by a perfect conductor such a discretization cannot in general approximate the singular behavior of the electromagnetic field near reentrant corners or edges the singular field method consists of adding to the finite element discretization space some particular fields which take into account the singular behavior the latter are deduced from the singular functions associated with the scalar laplace operator the theoretical justification of this approach as well as the analysis of the convergence of the approximation are presented for a very simple model problem arising from magnetostatics in a translation invariant setting but the study can be easily extended to numerous maxwell type problems the numerical implementation of both variants is studied for a domain containing a single reentrant corner

fully discrete finite element scheme for maxwell s equations with non linear boundary condition abstract we study a full maxwell s system accompanied with a non linear degenerate boundary condition which represents a generalization of the classical silver muller condition for a non perfect conductor the relationship between the normal components of electric e and magnetic h field obeys the following power law h e 1 e for some 0 1 we establish the existence and uniqueness of a weak solution in a suitable function spaces under the minimal regularity assumptions on the boundary and the initial data e 0 and h 0 we design a non linear time discrete approximation scheme and prove convergence of the approximations to a weak solution we also derive the error estimates for the time discretization as a next step we study the fully discrete problem using curl conforming edge elements and derive the corresponding error estimates finally we present some numerical experiments

a combined nodal continuous discontinuous finite element formulation for the maxwell problem abstract continuous galerkin formulations are appealing due to their low computational cost whereas discontinuous galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters since many electromagnetic problems involve materials with different physical properties this last point is very important for this reason in this article we have developed a combined cg dg formulation for maxwell s problem that allows arbitrary finite element spaces with functions continuous in patches of finite elements and discontinuous on the interfaces of these patches in particular the second formulation we propose comes from a novel continuous galerkin formulation that reduces the amount of stabilization introduced in the numerical system in all cases we have performed stability and convergence analyses of the methods the outcome of this work is a new approach that keeps the low cpu cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones all these methods have been tested using a problem with singular solution and another one with different materials in order to prove that in fact the resulting formulations can properly deal with these problems

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

a mixed method for approximating maxwell s equations a semidiscrete mixed finite element approximation to the time dependent maxwell s equations on a bounded smooth domain is analyzed a variational problem for the electric and magnetic fields in which the boundary conditions are enforced naturally is derived then a general convergence result for mixed methods is proven and it is shown how this result may be used to prove various error estimates when nedelec s curl conforming finite elements are used jz3 with connected boundary f and unit outward normal n let e x and 1 x denote respectively the dielectric constant and magnetic permeability of the medium occupying q let a x denote the conductivity of the medium then if e x t and h x t denote respectively the electric and magnetic fields maxwell s equations 10 state that

solving semidefinite quadratic linear programs using sdpt3 this paper discusses computational experiments with linear optimization problems involving semidefinite quadratic and linear cone constraints sqlps many test problems of this type are solved using a new release of sdpt3 a matlab implementation of infeasible primal dual path following algorithms the software developed by the authors uses mehrotra type predictor corrector variants of interior point methods and two types of search directions the hkm and nt directions a discussion of implementation details is provided and computational results on problems from the sdplib and dimacs challenge collections are reported

a singular field method for the solution of maxwell s equations in polyhedral domains it is well known that in the case of a regular domain the solution of the time harmonic maxwell s equations allows a discretization by means of nodal finite elements this is achieved by solving a regularized problem similar to the vector helmholtz equation the present paper deals with the same problem in the case of a nonconvex polyhedron it is shown that a nodal finite element method does not approximate in general the solution to maxwell s equations but actually the solution to a neighboring variational problem involving a different function space indeed the solution to maxwell s equations presents singularities near the edges and corners of the domain that cannot be approximated by lagrange finite elements a new method is proposed involving the decomposition of the solution field into a regular part that can be treated numerically by nodal finite elements and a singular part that has to be taken into account explicitly this singular field method is presented in various situations such as electri

the mortar finite element method for 3d maxwell equations first results in the framework of domain decomposition methods we extend the main ideas of the mortar element method to the numerical solution of maxwell s equations in wave form by h curl conforming finite elements the method we propose turns out to be a new nonconforming nonoverlapping domain decomposition method where nonmatching grids are allowed at the interfaces between subdomains a model problem is considered the convergence of the discrete approximation is analyzed and an error estimate is provided the method is proven to be slightly suboptimal with a loss of a factor scriptstyle sqrt rm ln h with respect to the degree of polynomials in order to achieve this convergence result we nevertheless need extra regularity assumptions on the solution of the continuous problem

expected residual minimization formulation for a class of stochastic linear second order cone complementarity problems abstract this paper considers a class of stochastic linear second order cone complementarity problems slsoccp noticing that the slsoccp does not have a solution suitable to all realizations in general we present a deterministic formulation called the expected residual minimization erm formulation for it the coercive property of the erm problem and the robustness of its solutions are discussed due to the existence of expectation in the erm problem we employ the monte carlo approximation techniques to approximate the erm problem and show that under mild conditions this approximation approach possesses exponential convergence rate then we extend the above results to a general mixed slsoccp furthermore we apply the theoretical results to a stochastic optimal power flow model in radial network and report some numerical dispatching experiments for real world southern california edison 47 bus network

convergence and quasi optimality of adaptive finite element methods for harmonic forms numerical computation of harmonic forms typically called harmonic fields in three space dimensions arises in various areas including computer graphics and computational electromagnetics the finite element exterior calculus framework also relies extensively on accurate computation of harmonic forms in this work we study the convergence properties of adaptive finite element methods afem for computing harmonic forms we show that a properly defined afem is contractive and achieves optimal convergence rate beginning from any initial conforming mesh this result is contrasted with related afem convergence results for elliptic eigenvalue problems where the initial mesh must be sufficiently fine in order for afem to achieve any provable convergence rate

convergence and optimality of adaptive edge finite element methods for time harmonic maxwell equations we consider a standard adaptive edge finite element method aefem based on arbitrary order nedelec edge elements for three dimensional indefinite time harmonic maxwell equations we prove that the aefem gives a contraction for the sum of the energy error and the scaled error estimator between two consecutive adaptive loops provided the initial mesh is fine enough using the geometric decay we show that the aefem yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom the main technical contribution of the paper is in the establishment of a quasi orthogonality and a localized a posteriori error estimator

uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism in this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains with a special emphasis for the case when the ratio between these coefficients is large in the most part of the work the interface between the two subdomains is supposed to be lipschitz we first study a scalar transmission problem which is handled through a converging asymptotic series then we derive uniform a priori estimates for maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material the technique is based on an appropriate decomposition of the electric field whose gradient part is estimated thanks to the first part as an application we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

on an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics in this work we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations the novelty of this formulation is the fact that it always converges to the physical solution even for singular ones a detailed set of numerical experiments have been performed in order to validate our approach

formulation and solution of some plasticity problems as conic programs abstract the application of conic programming to some traditionally difficult plasticity problems is considered convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given the types of yield criteria that can be treated by conic programming is discussed and it is shown that the three dimensional mohr coulomb criterion can be cast as a set of conic constraints thus facilitating efficient treatment by dedicated algorithms finally the performance of a number of mixed finite elements is evaluated together with a state of the art second order cone programming algorithm

well posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks we prove a regularity result for the anisotropic linear elasticity equation p u rm div left boldmath mathsf c cdot nabla u right f with mixed displacement and traction boundary conditions on a curved polyhedral domain omega subset mathbb r 3 in weighted sobolev spaces mathcal k m 1 a 1 omega for which the weight is given by the distance to the set of edges in particular we show that there is no loss of mathcal k m a regularity our curved polyhedral domains are allowed to have cracks we establish a well posedness result when there are no neighboring traction boundary conditions and a 0 that depends on p on the boundary conditions and on the domain our results extend to other strongly elliptic systems and higher dimensions

numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming summary the macroscopic strength properties of reinforced soils regarded as periodic composite materials are investigated by means of a fem based formulation of both static and kinematic approaches of yield design applied to the reinforced soil s unit cell because the reinforced soil s individual constituents obey a 3d mohr coulomb strength condition such a numerical problem can be treated through an optimization procedure using semidefinite programming the whole numerical procedure is applied to the derivation of both lower bound and upper bound estimates to the macroscopic yield surface of a soil reinforced either by columnar inclusions stone columns or a double array of trenches cross trench reinforcement the so obtained results highlight the efficiency of the proposed numerical method copyright 2014 john wiley sons ltd

a second order numerical scheme for nonlinear maxwell s equations using conforming finite element abstract in this paper we study and analyze a second order numerical scheme for maxwell s equations with nonlinear conductivity using the nedelec finite element method fem a purely explicit treatment of the nonlinear term greatly simplifies the computational effort since we only need to solve a constant coefficient linear system at each time step the curl conforming nature of the nedelec element assures its divergence free property in turn we present the linearized stability analysis for the numerical error function to obtain an optimal l2 error estimate in more details an o 2 h s error estimate in the l2 norm yields the maximum norm bound of the numerical solution so that the convergence analysis could be carried out at the next time step a few numerical examples in the transverse electric te case in two dimensional spaces are also presented which demonstrate the efficiency and accuracy of the proposed numerical scheme

time discretization scheme for quasi static maxwell s equations with a non linear boundary condition we study a time dependent eddy current equation for the magnetic field h accompanied with a non linear degenerate boundary condition bc which is a generalization of the classical silver muller condition for a non perfect conductor more exactly the relation between the normal components of electrical e and magnetic h fields obeys the following power law email protected email protected a email protected for some email protected 0 1 we establish the existence and uniqueness of a weak solution in a suitable function space under the minimal regularity assumptions on the boundary c and the initial data h 0 we design a non linear time discrete approximation scheme based on rothe s method and prove convergence of the approximations to a weak solution we also derive the error estimates for the time discretization

an adaptive multilevel method for time harmonic maxwell equations with singularities we develop an adaptive edge finite element method based on reliable and efficient residual based a posteriori error estimates for low frequency time harmonic maxwell equations with singularities the resulting discrete problem is solved by the multigrid preconditioned minres minimum residual iteration algorithm we demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which include in particular scattering over screens