an infinite dimensional purification principle without saturation abstract we establish a purification process for the min expected utilities coming from economy theory involved in the phenomenon of aversion to the ambiguity in game and decision theories we use instead of the saturation property a characterization of lyapunov infinite dimensional vector measures established in g knowles lyapunov vector measures siam j control 13 1975 294 303

distributional strategies for games with incomplete information we study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game theoretic models using the notion of distributional strategies we prove four main theorems i a mixed strategy nash equilibrium existence theorem ii a pure strategy equilibrium existence theorem iii a pure strategy equilibrium existence theorem and iv a theorem describing how the set of equilibria of a game varies with the parameters of the game

communication and equilibrium in discontinuous games of incomplete information this paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs typically the discontinuities arise from indeterminacies ties in the underlying problem the point of view taken here is that the tie breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model a solution is therefore a tie breaking rule together with strategies satisfying the usual best response criterion when information is incomplete solutions need not exist that is there may be no tie breaking rule that is compatible with the existence of strategy profiles satisfying the usual best response criteria it is shown that the introduction of incentive compatible communication cheap talk restores existence

a robust nitsche s formulation for interface problems abstract in this work we propose a novel weighting for the interfacial consistency terms arising in a nitsche variational form we demonstrate through numerical analysis and extensive numerical evidence that the choice of the weighting parameter has a great bearing on the stability of the method consequently we propose a weighting that results in an estimate for the stabilization parameter such that the method remains well behaved in varied settings ranging from the configuration of embedded interfaces resulting in arbitrarily small elements to such cases where a large contrast in material properties exists an important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of a elements with arbitrarily small volume fractions b large material heterogeneities and c both large heterogeneities as well as arbitrarily small elements we then highlight the accuracy and efficiency of the proposed formulation through numerical examples focusing particular attention on interfacial quantities of interest

spectral convergence and nonlinear dynamics of reaction diffusion equations under perturbations of the domain abstract in this paper we obtain the continuity of attractors for semilinear parabolic problems with neumann boundary conditions relatively to perturbations of the domain we show that if the perturbations on the domain are such that the convergence of eigenvalues and eigenfunctions of the neumann laplacian is granted then we obtain the upper semicontinuity of the attractors if moreover every equilibrium of the unperturbed problem is hyperbolic we also obtain the continuity of attractors we also give necessary and sufficient conditions for the spectral convergence of neumann problems under perturbations of the domain

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

nonatomic games on loeb spaces in the setting of noncooperative game theory strategic negligibility of individual agents or diffuseness of information has been modeled as a nonatomic measure space typically the unit interval endowed with lebesgue measure however recent work has shown that with uncountable action sets for example the unit interval there do not exist pure strategy nash equilibria in such nonatomic games in this brief announcement we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces hyperfinite loeb spaces we also emphasize other desirable properties of games on hyperfinite loeb spaces and present a synthetic treatment embracing both large games as well as those with incomplete information

high order gradients with the shifted boundary method an embedded enriched mixed formulation for elliptic pdes abstract we propose an extension of the embedded boundary method known as shifted boundary method to elliptic diffusion equations in mixed form e g darcy flow heat diffusion problems with rough coefficients etc our aim is to obtain an improved formulation that for linear finite elements is at least second order accurate for both flux and primary variable when either dirichlet or neumann boundary conditions are applied following previous work of nishikawa and mazaheri in the context of residual distribution methods we consider the mixed form of the diffusion equation i e with darcy type operators and introduce an enrichment of the primary variable this enrichment is obtained exploiting the relation between the primary variable and the flux variable which is explicitly available at nodes in the mixed formulation the proposed enrichment mimics a formally quadratic pressure approximation although only nodal unknowns are stored similar to a linear finite element approximation we consider both continuous and discontinuous finite element approximations and present two approaches a non symmetric enrichment which as in the original references only improves the consistency of the overall method and a symmetric enrichment which enables a full error analysis in the classical finite element context combined with the shifted boundary method these two approaches are extended to high order embedded computations and enable the approximation of both primary and flux gradient variables with second order accuracy independently on the type of boundary conditions applied we also show that the the primary variable is third order accurate when pure dirichlet boundary conditions are embedded

the effect of domain squeezing upon the dynamics of reaction diffusion equations abstract let be an arbitrary smooth bounded domain in r m r n and e 0 be arbitrary write x y for a generic point of r m r n squeeze by the factor e in the y direction to obtain the squeezed domain e x ey x y consider the following reaction diffusion equation on e formula here e is the exterior normal vector field on e and f r r is a nonlinearity satisfying some growth and dissipativeness conditions assuring such that ee generates a semiflow on h1 e with a global attractor a e we prove that in some strong sense the equations ee have a limiting equationu au f u e0 as e 0 this limiting equation is an abstract semilinear parabolic equation which defines a semiflow on a closed linear subspace of h1 we show that has a global attractor a 0 and the family of attractors a e e 0 is upper semicontinuous at e 0 if m n 1 and satisfies some natural additional assumptions then the limiting equation e0 is equivalent to a parabolic boundary value problem defined on a finite graph the results of this paper extend previous results obtained by hale and raugel for domains which are ordinate sets of a positive function

asymptotic behavior of stochastic fitzhugh nagumo systems on unbounded thin domains abstract this article is concerned with the asymptotic behavior of solutions of a class of non autonomous stochastic fitzhugh nagumo systems driven by multiplicative white noise on unbounded thin domains the existence and uniqueness of tempered pullback random attractors are proved for the systems defined on n 1 dimensional unbounded narrow domains we also establish the upper semicontinuity of these attractors when a family of n 1 dimensional unbounded thin domains collapses onto an n dimensional unbounded domain a cut off method and a decomposition technique are employed to derive the pullback asymptotic compactness of solutions in order to overcome the difficulties caused by the non compactness of sobolev embeddings on unbounded domains as well as the lack of regularity of one component of the solutions

a reduced order shifted boundary method for parametrized incompressible navier stokes equations abstract we investigate a projection based reduced order model of the steady incompressible navier stokes equations for moderate reynolds numbers in particular we construct an embedded reduced basis space by applying proper orthogonal decomposition to the shifted boundary method a high fidelity embedded method recently developed we focus on the geometrical parametrization through level set geometries using a fixed cartesian background geometry and the associated mesh this approach avoids both remeshing and the development of a reference domain formulation as typically done in fitted mesh finite element formulations two dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach

neumann spectral problem in a domain with very corrugated boundary let rn be a bounded domain we perturb it to a domain e attaching a family of small protuberances with room and passage like geometry e 0 is a small parameter peculiar spectral properties of neumann problems in so perturbed domains were observed for the first time by r courant and d hilbert we study the case when the number of protuberances tends to infinity as e 0 and they are e periodically distributed along a part of our goal is to describe the behavior of the spectrum of the operator ae e 1 e where e is the neumann laplacian in e and the positive function e is equal to 1 in we prove that the spectrum of ae converges as e 0 to the spectrum of a certain boundary value problem for the neumann laplacian in with boundary conditions containing the spectral parameter in a nonlinear manner its eigenvalues may accumulate to a finite point

approximate purification of mixed strategies under relatively weak conditions on the information structure of a game it is shown that any mixed strategy of a player can be replaced by a certain pure strategy without affecting any player s expected payoff appreciably no matter what strategies the other players use under even weaker conditions the existence of a nash equilibrium in mixed strategies is shown to guarantee the existence of a pure strategy combination which is an approximate equilibrium

limiting behavior of non autonomous stochastic reaction diffusion equations on thin domains abstract this paper deals with the limiting behavior of stochastic reaction diffusion equations driven by multiplicative noise and deterministic non autonomous terms defined on thin domains we first prove the existence uniqueness and periodicity of pullback tempered random attractors for the equations in an n 1 dimensional narrow domain and then establish the upper semicontinuity of these attractors when a family of n 1 dimensional thin domains collapses onto an n dimensional domain

a face oriented stabilized nitsche type extended variational multiscale method for incompressible two phase flow a novel extended variational multiscale method for incompressible two phase flow is proposed in this approach the level set method which allows for accurately representing complex interface evolutions is combined with an extended finite element method for the fluid field sharp representation of the discontinuities at the interface related to surface tension effects and large material parameter ratios are enabled by this approach to capture the discontinuities jump enrichments are applied for both velocity and pressure field nitsche s method is then used to weakly impose the continuity of the velocity field for a stable formulation on the entire domain residual based variational multiscale terms are supported by appropriate face oriented ghost penalty and fluid stabilization terms in the region of enriched elements both face oriented terms as well as interfacial terms related to nitsche s method are introduced such that it is accounted for viscous and convection dominated transient flows as a result stability and wellconditioned systems are guaranteed independent of the interface location the proposed method is applied to four numerical examples of increasing complexity two dimensional rayleigh taylor instabilities a twodimensional collapsing water column three dimensional rising bubbles as well as a three dimensional bubble coalescence excellent agreement with either analytical solutions or numerical and experimental reference data as well as robustness for all flow regimes is demonstrated for all examples

asymptotic behavior of a parabolic problem with terms concentrated in the boundary abstract we analyze the asymptotic behavior of the attractors of a parabolic problem when some reaction and potential terms are concentrated in a neighborhood of a portion of the boundary and this neighborhood shrinks to as a parameter e goes to zero we prove that this family of attractors is upper continuous at e 0

the second generation shifted boundary method and its numerical analysis abstract recently the shifted boundary method sbm was proposed within the class of unfitted or immersed or embedded finite element methods by reformulating the original boundary value problem over a surrogate approximate computational domain the sbm avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning accuracy is maintained by modifying the original boundary conditions using taylor expansions hence the name of the method that shifts the location and values of the boundary conditions in this article we present enhanced variational sbm formulations for the poisson and stokes problems with improved flexibility and robustness these simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations first we show that these new sbm implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive second we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at dirichlet boundaries therefore avoiding the calibration of an additional stabilization parameter finally we prove enhanced l 2 estimates without the cumbersome assumption of earlier proofs that the surrogate domain is convex instead we rely on a conventional assumption that the boundary of the true domain is smooth which can also be replaced by requiring convexity of the true domain the aforementioned improvements open the way to a more general and efficient implementation of the shifted boundary method particularly in complex three dimensional geometries we complement these theoretical developments with numerical experiments in two and three dimensions

a nitsche method for wave propagation problems in time domain we propose a new nitsche type approach for the weak enforcement of dirichlet and neumann boundary conditions in the context of time domain wave propagation problems in mixed form a peculiar feature of the proposed method is that due to the hyperbolic structure of the problem considered two penalty parameters are introduced corresponding to dirichlet and neumann conditions respectively a stability and convergence estimate is also provided in the case of a discontinuous in time galerkin space time integrator the spatial discretization used is based on a stabilized method with equal order interpolation for all solution components in principle however the proposed methodology is not confined to stabilized methods we conclude with an extensive set of tests to validate the robustness and accuracy of the proposed approach

uniform resolvent convergence for strip with fast oscillating boundary abstract in a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small on the oscillating boundary we impose dirichlet neumann or robin boundary condition in all cases we describe the homogenized operator establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one and prove the estimates for the rate of convergence these results are obtained as the order of the amplitude of the oscillations is less equal or greater than that of the period it is shown that under the homogenization the type of the boundary condition can change

weighted extended b spline approximation of dirichlet problems we describe a new finite element method which uses weighted extended b splines on a regular grid as basis functions for solving dirichlet problems on bounded domains in arbitrary dimensions this web method does not require any grid generation and can be implemented very efficiently it yields smooth high order accurate approximations with relatively low dimensional subspaces

semilinear parabolic problems in thin domains with a highly oscillatory boundary abstract in this paper we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment thin domain which has an oscillating boundary we combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations

continuum theory of epitaxial crystal growth i we present various continuum limits to describe epitaxial thin film growth we consider a hierarchy of models which can take into account the diffusion of terrace adatoms attachment and detachment of edge adatoms vapor phase diffusion and the effect of multiple species the starting point is the burton cabrera frank type step flow model we have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a hamilton jacobi equation for the film height function this is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film the results here can be used in a macroscopic description of thin film growth

finite element simulation of non linear sound wave propagation abstract a numerical approach for non linear acoustic wave propagation is proposed in which a finite element method is used an approximate equation which can describe the effect of diffraction with reasonable accuracy is derived based on the equations of fluid dynamics only the generation of the second harmonic wave is considered with the higher order harmonics being neglected under the assumption of weak non linearity a set of uncoupled equations for the primary and secondary wave is discretized in space by a finite element method and then solved by using the newmark integration scheme for time only two dimensional cases are considered and some numerical examples are presented for sound propagation along a duct with stepped width for scattering from a circular rod and for a focusing source in which the diffraction effect is of interest some examples of the wave propagation fields are displayed

average of the navier s law on the rapidly oscillating boundary we study the flow of newtonian fluid in a domain with periodically wrinkled boundary with slip navier s boundary condition the goal of this paper is to replace a microscopic boundary condition posed on the rough boundary by some macroscopic boundary condition posed on the middle surface of the oscillating boundary depending on the shape of wrinkles and the friction coefficient we get four different effective models

an unfitted finite element method based on nitsche s method for elliptic interface problems in this paper we propose a method for the finite element solution of elliptic interface problem using an approach due to nitsche the method allows for discontinuities internal to the elements in the approximation across the interface we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh further we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

on the limits of communication in multidimensional cheap talk a comment we analyze a cheap talk game a la crawford and sobel in a multidimensional state and policy space a feature of the multidimensional state space is that communication on one dimension often reveals information on others we show how this feature imposes bounds on communication

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

the neumann problem in thin domains with very highly oscillatory boundaries abstract in this paper we analyze the behavior of solutions of the neumann problem posed in a thin domain of the type r x 1 x 2 r 2 x 1 0 1 b x 1 x 2 g x 1 x 1 with 1 and 0 defined by smooth functions b x and g x y where the function g is supposed to be l x periodic in the second variable y the condition 1 implies that the upper boundary of this thin domain presents a very high oscillatory behavior indeed we have that the order of its oscillations is larger than the order of the amplitude and height of r given by the small parameter we also consider more general and complicated geometries for thin domains which are not given as the graph of certain smooth functions but rather more comb like domains

the finite cell method for three dimensional problems of solid mechanics this article presents a generalization of the recently proposed finite cell method to three dimensional problems of linear elasticity the finite cell method combines ideas from embedding or fictitious domain methods with the p version of the finite element method besides supporting a fast simple generation of meshes it also provides high convergence rates mesh generation for a boundary representation of solids and for voxel based data obtained from ct scans is addressed in detail in addition the implementation of non homogeneous neumann boundary conditions and the computation of cell matrices based on a composed integration is presented the performance of the proposed method is demonstrated by three numerical examples including the elastostatic computation of a human bone biopsy

dynamics in dumbbell domains iii continuity of attractors in this paper we conclude the analysis started in 3 and continued in 4 con cerning the behavior of the asymptotic dynamics of a dissipative reactions di usion equation in a dumbbell domain as the channel shrinks to a line segment in 3 we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria in 4 we have analyzed the behavior of the limiting problem in this paper we show that the attractors are upper semicontinuous and moreover if all equilibria of the limiting problem are hyperbolic then they are lower semicontinuous and therefore continuous the continuity is obtained in lp and h1 norms

fractional problems in thin domains abstract in this paper we consider nonlocal fractional problems in thin domains given open bounded subsets u r n and v r m we show that the solution u e to x s u e x y y t u e x y f x e 1 y in u e v with u e x y 0 if x u and y e v verifies that u e x y u e x e y u 0 strongly in the natural fractional sobolev space associated to this problem we also identify the limit problem that is satisfied by u 0 and estimate the rate of convergence in the uniform norm here x s u and y t u are the fractional laplacian in the 1st variable x with a dirichlet condition u x 0 if x u and in the 2nd variable y with a neumann condition integrating only inside v respectively that is x s u x y r n u x y u w y x w n 2 s d w and y t u x y v u x y u x z y z m 2 t d z

the shifted boundary method for embedded domain computations part i poisson and stokes problems abstract we propose a new finite element method for embedded domain computations which falls in the category of surrogate approximate boundary algorithms the key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary and to appropriately modify the shifted boundary conditions enforced weakly in order to preserve optimal convergence rates of the numerical solution this process yields a method which in our view is simple efficient and also robust since it is not affected by the small cut cell problem although general in nature here we apply this new concept to the poisson and stokes problems we present in particular the full analysis of stability and convergence for the case of the poisson operator and numerical tests for both the poisson and stokes equations for geometries of progressively higher complexity

a new 3 d numerical approach to the solution of pdes with optimal accuracy on irregular domains and cartesian meshes abstract a new 3 d numerical approach for the time dependent wave and heat equations as well as for the time independent laplace equation on irregular domains with the dirichlet boundary conditions has been developed trivial cartesian meshes and simple 27 point uniform and nonuniform stencil equations are used for 3 d irregular domains the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique very small distances 0 1 h 1 0 9 h where h is the grid size between the grid points of a cartesian mesh and the boundary do not worsen the accuracy of the new technique at similar 27 point stencils the accuracy of the new approach is two orders higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the fifth order tetrahedral finite elements with much wider stencils the wave and heat equations can be uniformly treated with the new approach the order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi discrete systems the new approach can be directly applied to other partial differential equations

weak boundary conditions for wave propagation problems in confined domains formulation and implementation using a variational multiscale method abstract we propose a new approach to the enforcement of dirichlet neumann or robin boundary conditions in finite element computations of wave propagation problems the key idea is to enforce the boundary conditions weakly as part of the variational formulation due to the hyperbolic structure of the problem considered the variational formulation does not require any penalty parameters in contrast with what typically happens in elliptic or advection diffusion parabolic problems this article presents the implementation of the proposed boundary condition framework using a variational multiscale method for the wave equation in mixed form we conclude with an extensive set of tests to validate the robustness and accuracy of the proposed approach

the boundary value problem in domains with very rapidly oscillating boundary abstract we study the asymptotic behavior of the solution to boundary value problem for the second order elliptic equation in the bounded domain e rnwith a very rapidly oscillating locally periodic boundary we assume that the fourier boundary condition involving a small positive parameter e is posed on the oscillating part of the boundary and that the n 1 dimensional volume of this part goes to infinity as e 0 under proper normalization conditions that homogenized problem is found and the estimates of the residual are obtained also we construct an additional term of the asymptotics to improve the estimates of the residual it is shown that the limiting problem can involve dirichlet fourier or neumann boundary conditions depending on the structure of the coefficient of the original problem

an explicit residual based approach for shallow water flows we describe fully explicit residual based discretizations of the shallow water equations with friction on unstructured grids the schemes are obtained by properly adapting the explicit construction proposed in ricchiuto and abgrall 2010 57 in particular previous work on well balanced integration ricchiuto 2011 56 and preservation of the depth non negativity ricchiuto and bollermann 2009 60 is reformulated in the context of a genuinely explicit time stepping still based on a weighted residual approximation the paper discusses in depth how to achieve in this context an exact preservation of all the simple known steady equilibria and how to obtain a super consistent approximation for smooth non trivial moving equilibria the treatment of the wetting drying interface is also discussed giving formal conditions for the preservation of the non negativity of the depth for a particular case based on a nonlinear variant of a lax friedrichs type scheme the approach is analyzed and tested thoroughly the quality of the numerical results shows the interest in the proposed approach over previously proposed schemes in terms of accuracy and efficiency

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

limiting dynamics for stochastic reaction diffusion equations on the sobolev space with thin domains abstract this paper is devoted to bi spatial random attractors of the stochastic reaction diffusion equation when the terminate space is the sobolev space on a thin domain where the nonlinearity can be decomposed into two functions with p q growth exponents by means of a computation method of induction it is shown that the difference of solutions near the initial time is integrable of k p 2 k 2 order this higher order integrability shows continuity of the solution operator from the square lebesgue space to k p 2 k 2 order lebesgue spaces in particular the 2 p 2 order integrability shows continuity of the solution operator from the square lebesgue space to the sobolev space which further shows existence of a random attractor in the sobolev space when the initial space is the square lebesgue space moreover the higher order integrability can be uniform with respect to all thin domains which provides uniformly asymptotic compactness of the random dynamical systems as a conclusion the upper semi continuity of attractors under the sobolev norm is established when the narrow domain degenerates onto a lower dimensional domain

numerical approximation of laminar flows over rough walls with sharp asperities abstract we consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall the latter is assumed to consist of a plane wall covered with periodically distributed asperities whose size depends on a small parameter e 0 the assumption of sharp asperities is made that is the height of the asperities does not vanish as e 0 the rough wall is at rest and the plane wall is moving at a constant horizontal velocity we assume that the flow is governed by the stationary stokes equations we give an asymptotic approximation of the stokes flow under the rugose region by a couette flow depending on the size e of the asperities we then build a numerical approximation of the couette flow based on a partial domain decomposition method

semilinear elliptic equations in thin domains with reaction terms concentrating on boundary abstract in this paper we analyze the behavior of a family of steady state solutions of a semilinear reaction diffusion equation with homogeneous neumann boundary condition posed in a two dimensional thin domain with reaction terms concentrated in a narrow oscillating neighborhood of the boundary we assume that the domain and therefore the oscillating boundary neighborhood degenerates into an interval as a small parameter goes to zero our main result is that this family of solutions converges to the solution of a one dimensional limit equation capturing the geometry and oscillatory behavior of the open sets where the problem is established

effective boundary condition for stokes flow over a very rough surface abstract the main purpose of this paper is to derive a wall law for a flow over a very rough surface we consider a viscous incompressible fluid filling a 3 dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a very rough wall the latter consists in a plane wall covered with periodically distributed asperities which size depends on a small parameter e 0 and with a fixed height we assume that the flow is governed by the stationary stokes equations using asymptotic expansions and boundary layer correctors we construct and analyze an asymptotic approximation of order o e 3 2 0 being arbitrary small in the h 1 norm for the velocity and in the l 2 norm for the pressure we derive an effective boundary condition of navier type then expressing the boundary layer terms in terms of the homogenized solution and the solution of a cell problem we obtain an effective approximation in the whole domain of the flow

the shifted boundary method for embedded domain computations part ii linear advection diffusion and incompressible navier stokes equations abstract we propose a new embedded finite element method for the linear advection diffusion equation and the laminar and turbulent incompressible navier stokes equations the proposed method belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates we include the full analysis of stability and convergence of the method in the linear advection diffusion equation and a battery of tests for the case of laminar and turbulent incompressible navier stokes equations we also discuss the conservation properties of the proposed method in all cases

dynamics in dumbbell domains i continuity of the set of equilibria we analyze the dynamics of a reaction diffusion equation with homogeneous neumann boundary conditions in a dumbbell domain we provide an appropriate functional setting to treat this problem and as a first step we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds

subdivision stabilised immersed b spline finite elements for moving boundary flows an immersed finite element method is presented to compute flows with complex moving boundaries on a fixed cartesian grid the viscous incompressible fluid flow equations are discretized with b spline basis functions the two scale relation for b splines is used to implement an elegant and efficient technique to satisfy the lbb condition on non grid aligned fluid domains and at moving boundaries the boundary conditions are enforced with a consistent penalty method as originally proposed by nitsche in addition a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut cells the versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations

the best sobolev trace constant in a domain with oscillating boundary abstract in this paper we study homogenization problems for the best constant for the sobolev trace embedding w 1 p l q in a bounded smooth domain when the boundary is perturbed by adding an oscillation we find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary for sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations

spectrum of a singularly perturbed periodic thin waveguide abstract we consider a family e e 0 of periodic domains in r 2 with waveguide geometry and analyse spectral properties of the neumann laplacian e on e the waveguide e is a union of a thin straight strip of the width e and a family of small protuberances with the so called room and passage geometry the protuberances are attached periodically with a period e along the strip upper boundary we prove a kind of resolvent convergence of e to a certain operator on the line as e 0 also we demonstrate hausdorff convergence of the spectrum in particular we conclude that if the sizes of passages are appropriately scaled the first spectral gap of e is determined exclusively by geometric properties of the protuberances the proofs are carried out using methods of homogenization theory

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

analysis of the shifted boundary method for the stokes problem abstract the analysis of stability and accuracy of the shifted boundary method is developed for the stokes flow equations the key feature of the shifted boundary method an embedded finite element method is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary and an appropriate modification shifting of the value of the boundary conditions an inf sup condition is proved for the variational formulation associated to the shifted boundary method and we derive by way of strang s second lemma an optimal error estimate in the natural sbm norm we also derive an l 2 error estimate for the velocity field by means of an extension of the aubin nitsche approach to embedded non consistent mixed finite element methods

suboptimal solutions to team optimization problems with stochastic information structure existence uniqueness and approximations of smooth solutions to team optimization problems with stochastic information structure are investigated suboptimal strategies made up of linear combinations of basis functions containing adjustable parameters are considered estimates of their accuracies are derived by combining properties of the unknown optimal strategies with tools from nonlinear approximation theory the estimates are obtained for basis functions corresponding to sinusoids with variable frequencies and phases gaussians with variable centers and widths and sigmoidal ridge functions the theoretical results are applied to a problem of optimal production in a multidivisional firm for which numerical simulations are presented

the shifted boundary method for hyperbolic systems embedded domain computations of linear waves and shallow water flows abstract we propose a new computational approach for embedded boundary simulations of hyperbolic systems and in particular the linear wave equations and the nonlinear shallow water equations the proposed approach belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates this framework is applied here in the setting of a stabilized finite element method even though other spatial discretization techniques could have been employed accuracy stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations comparisons with standard weak boundary conditions imposed on body fitted grids which conform to the geometry of the computational domain boundaries are also presented

dynamics in dumbbell domains ii the limiting problem in this work we continue the analysis of the asymptotic dynamics of reaction diffusion problems in a dumbbell domain started in j m arrieta a n carvalho g lozada cruz dynamics in dumbbell domains i continuity of the set of equilibria j differential equations 231 2 2006 551 597 here we study the limiting problem that is an evolution problem in a domain which consists of an open bounded and smooth set rn with a curve r0 attached to it the evolution in both parts of the domain is governed by a parabolic equation in the evolution is independent of the evolution in r0 whereas in r0 the evolution depends on the evolution in through the continuity condition of the solution at the junction points we analyze in detail the linear elliptic and parabolic problem the generation of linear and nonlinear semigroups the existence and structure of attractors

the treatment of the neumann boundary conditions for a new numerical approach to the solution of pdes with optimal accuracy on irregular domains and cartesian meshes abstract recently we have developed a new 3 d numerical approach for the time dependent wave and heat equations as well as for the time independent poisson equation on irregular domains with the dirichlet boundary conditions its extension to the neumann boundary conditions that was a big issue due to the presence of normal derivatives along irregular boundaries is considered in this paper trivial cartesian meshes and simple 27 point uniform and nonuniform stencil equations are used with the new approach for 3 d irregular domains the neumann boundary conditions are introduced as the known right hand side into the stencil and do not change the width of the stencil the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique very small distances 0 1 h 1 0 9 h where h is the grid size between the grid points of a cartesian mesh and the boundary do not worsen the accuracy of the new technique at similar 27 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the fourth order tetrahedral finite elements with much wider stencils the wave and heat equations can be uniformly treated with the new approach the order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi discrete systems the new approach can be directly applied to other partial differential equations

nonlocal problems in thin domains in this paper we consider nonlocal problems in thin domains first we deal with a nonlocal neumann problem that is we study the behavior of the solutions to f x 1 2j x y u y u x dyf x 1 2j x y u y u x dy with j z j z1 z2 j z j z1 z2 and 1 2 rn rn1 rn2 1 2 rn rn1 rn2 a bounded domain we find that there is a limit problem that is we show that u u0u u0 as 0 0 in and this limit function verifies 2f x1 x2 dx2 2 1j x1 y1 0 u0 y1 u0 x1 dy1 with u0 x1 2u0 x1 x2 dx2 in addition we deal with a double limit when we add to this model a rescale in the kernel with a parameter that controls the size of the support of j we show that this double limit exhibits some interesting features we also study a nonlocal dirichlet problem f x rnj x y u y u x dy x x with u x 0u x 0 x rn x rn and deal with similar issues in this case the limit as 0 0 is u0 0u0 0 and the double limit problem commutes and also gives v 0v 0 at the end

continuity of attractors for a reaction diffusion problem with nonlinear boundary conditions with respect to variations of the domain in this work we show for a class of dissipative semilinear parabolic problems that the global compact attractor varies continuously with respect to parameters in the equations applications to a parabolic problem with nonlinear boundary conditions are also obtained

on the existence of monotone pure strategy equilibria in bayesian games we extend and strengthen both athey s 2001 and mcadams 2003 results on the existence of monotone pure strategy equilibria in bayesian games we allow action spaces to be compact locally complete metrizable semilatttices and can handle both a weaker form of quasisupermodularity than is employed by mcadams and a weaker single crossing property than is required by both athey and mcadams our proof which is based upon contractibility rather than convexity of best reply sets demonstrates that the only role of single crossing is to help ensure the existence of monotone best replies finally we do not require the milgrom weber 1985 absolute continuity condition on the joint distribution of types

singular limit for a nonlinear parabolic equation with terms concentrating on the boundary abstract we analyze the asymptotic behavior of the attractors of a parabolic problem when some reaction and potential terms are concentrated in a neighborhood of a portion of the boundary and this neighborhood shrinks to as a parameter e goes to zero we prove that the family of attractors is upper continuous at the e 0

boundary type finite element method for surface wave motion based on trigonometric function interpolation there are many physical phenomena which can be handled by the helmholtz equation the equation explains certain phenomena of wave propagation this paper presents a new finite element method to analyse surface wave motion the characteristic point of this method is that the interpolation equation is chosen to satisfy the governing helmholtz equation using trigonometric functions this follows that the variational functional to be minimized can be formulated such that the integration is limited to the boundary of the element the numerical solutions obtained are compared with analytical and experimental solutions from these comparative studies it is concluded that the present method provides a useful tool for the analysis of surface wave motion

prediction of wall pressure fluctuation in turbulent flows with an immersed boundary method the objective of this paper is to assess the accuracy and efficiency of the immersed boundary ib method to predict the wall pressure fluctuations in turbulent flows where the flow dynamics in the near wall region is fundamental to correctly predict the overall flow the present approach achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous ib methods by introducing additional constraints a compatibility for the interpolated velocity boundary condition related to mass conservation and the formal decoupling of the pressure on this surfaces the immersed boundary approximated domain method ib adm developed in the present study satisfies these conditions with an inexpensive computational overhead the ib adm correctly predicts the near wall velocity pressure and scalar fields in several example problems including flows around a very thin solid object for which incorrect results were obtained with previous ib methods in order to have sufficient near wall mesh resolution for les and dns computations the present approach uses local mesh refinement the present method has been also successfully applied to computation of the wall pressure space time correlation in dns of turbulent channel flow on grids not aligned with the boundaries when applied to a turbulent flow around an airfoil the computed flow statistics the mean rms flow field and power spectra of the wall pressure are in good agreement with experiment

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

thin domains with non smooth periodic oscillatory boundaries abstract in this work we study in detail how to adapt the unfolding operator method to thin domains with periodic oscillatory boundaries we present the unfolding method as a general approach which allows us to analyze the behavior of the solutions of a neumann problem for equation u u f posed in two dimensional thin domains with an oscillatory boundary assuming very mild hypothesis on the regularity of the oscillatory boundary we obtain the homogenized limit problem and corrector results for the three different cases depending on the order of the period of the oscillations

robin type boundary conditions in transition from reaction diffusion equations in 3d domains to equations in 2d domains abstract we consider a singular limit of diffusion equations in 3d domains of thickness converging to zero in the 2d limit the resulting reaction diffusion equation has a source term resulting from the robin type boundary conditions imposed on boundaries of the original 3d domain the proposed approach can be applied to constructing approximate solutions of diffusion problems in thin planar cylindrical or spherical layers between two membranes as an example we refer to the problem of activation of b lymphocytes which typically have large nuclei and a thin cytoplasmic layer which can be considered as a spherical shell for this example assuming additionally axial symmetry we provide a rigorous convergence theorem in the language of semigroups of operators

uniform continuity of the value of zero sum games with differential information we establish uniform continuity of the value for zero sum games with differential information when the distance between changing information fields of each player is measured by the boylan pseudometric we also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change even with the weak topology on players strategy sets and is approximately lower semicontinuous

projection based reduced order models for a cut finite element method in parametrized domains abstract this work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method such methods and in particular the cutfem method are attractive in the generation of projection based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes the combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems avoiding remeshing as well as the reference domain formulation often used in the reduced order modeling for boundary fitted finite element formulations the resulting novel methodology is presented on linear elliptic and stokes problems together with several test cases to assess its capability the role of a proper extension and transport of embedded solutions to a common background is analyzed in detail

limiting behavior of non autonomous stochastic reaction diffusion equations on unbounded thin domains this article is concerned with the limiting behavior of dynamics of a class of nonautonomous stochastic partial differential equations driven by multiplicative white noise on unbounded thin domains we first prove the existence of tempered pullback random attractors for the equations defined on n 1 dimensional unbounded thin domains then we show the upper semicontinuity of these attractors when the n 1 dimensional unbounded thin domains collapse onto the n dimensional space rn here the tail estimates are utilized to deal with the noncompactness of sobolev embeddings on unbounded domains

a zero sum game with incomplete information and compact action spaces we make use of distributional strategies to describe player s choices of actions in a zero sum game with incomplete information and compact action spaces under very mild assumptions we obtain the existence of equilibria

homogenization of the brush problem with a source term in l 1 we consider a domain which has the form of a brush in 3d or the form of a comb in 2d i e an open set which is composed of cylindrical vertical teeth distributed over a fixed basis all the teeth have a similar fixed height their cross sections can vary from one teeth to another one and are not supposed to be smooth moreover the teeth can be adjacent i e they can share parts of their boundaries the diameter of every tooth is supposed to be less than or equal to e and the asymptotic volume fraction of the teeth as e tends to zero is supposed to be bounded from below away from zero but no periodicity is assumed on the distribution of the teeth in this domain we study the asymptotic behavior as e tends to zero of the solution of a second order uniformly elliptic equation with a zeroth order term which is bounded from below away from zero when the homogeneous neumann boundary condition is satisfied on the whole of the boundary first we revisit the problem where the source term belongs to l 2 this is a classical problem but our homogenization result takes place in a geometry which is more general that the ones which have been considered before moreover we prove a corrector result which is new then we study the case where the source term belongs to l 1 working in the framework of renormalized solutions and introducing a definition of renormalized solutions for degenerate elliptic equations where only the vertical derivative is involved such a definition is new we identify the limit problem and prove a corrector result

cheap talk and sequential equilibria in signaling games well behaved infinite signaling games may have no sequential equilibria we prove that adding cheap talk to these games solves the nonexistence problem the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap talk extension of the limit game in addition when the signaling space has no isolated points any cheap talk sequential equilibrium outcome can be approximated by a sequential e equilibrium of the game without cheap talk

a high order numerical approach with cartesian meshes for modeling of wave propagation and heat transfer on irregular domains with inhomogeneous materials abstract recently we have developed a new numerical approach for pdes with constant coefficients on irregular domains and cartesian meshes in this paper we extend it to a much more general case of pdes with variable coefficients that have a lot of applications e g the modeling of functionally graded materials the inhomogeneous materials obtained by 3 d printing and many others here we consider the 2 d wave and heat equations for isotropic and anisotropic inhomogeneous materials the idea of the extension to the case of pdes with variable coefficients is based on the representation of the stencil coefficients as functions of the mesh size this leads to the increase in the size of the local system of algebraic equations solved for each grid point of the new approach however this does not change the size of the global system of semidiscrete equations and practically does not increase the computational costs of the proposed technique similar to our previous technique the new 2 d approach with compact 9 point stencils uses trivial cartesian meshes for complex irregular domains and provides the fourth order of accuracy for the wave and heat equations with variable coefficients the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique at similar 9 point stencils the accuracy of the new approach is much higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the third order finite elements with much wider stencils the wave and heat equations are uniformly treated with the new approach

semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries abstract in this work we study the behavior of a family of solutions of a semilinear elliptic equation with homogeneous neumann boundary condition posed in a two dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary our main result is concerned with the upper and lower semicontinuity of the set of solutions we show that the solutions of our perturbed equation can be approximated with one of a one dimensional equation which also captures the effects of all relevant physical processes that take place in the original problem