In this paper a Nitsche-type discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region Ω which is a union of N disjoint polygonal subdomains Ωi of diameter O(Hi). The discontinuities of the coefficients, possibly very large, are assumed to occur only across the subd...

We extend several known results on solvability in the Sobolev spaces W 1 p , p ∈ [2,∞), of SPDEs in divergence form in R d + to equations having coefficients which are discontinuous in the space variable.

We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in R and a corresponding example for a Stokes-like system.

This note aims to give a brief account on some recent progress of the simulation techniques of stochastic processes associated to divergence-form opertors with discontinuous coefficients, such as the one used in the Darcy law.

Abstract. We rigorously prove results on spiky patterns for the Gierer-Meinhardt system [8] with a jump discontinuity in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt [1], [3], [11]. Firstly, we show the existence of an interior spike located away fr...

This article is devoted to obtain the Γ-limit, as ε tends to zero, of the family of functionals u 7→ ∫ Ω f ( x, x ε , . . . , x ε ,∇u(x) ) dx, where f = f(x, y, . . . , yn, z) is periodic in y, . . . , yn, convex in z and satisfies a very weak regularity assumption with respect to x, y, . . . , yn. We approach the problem using the multiscale Young measures.

For the numerical simulation in continuum mechanics the Composite Finite Element (CFE) method allows an effective treatment of problems where material parameters are discontinuous across geometrically complicated interfaces. Instead of complicated and computationally expensive tetrahedral meshing, specialized CFE basis functions are constructed on a uniform hexahedral grid. This is a convenient...

We consider a second-order elliptic equation with discontinuous or anisotropic coefficients in a bounded twoor three dimensional domain, and its finiteelement discretization. The aim of this paper is to prove some a priori and a posteriori error estimates in an appropriate norm, which are independent of the variation of the coefficients. Résumé: Nous considérons une équation elliptique du secon...