N–N Solvers for a DG Discretization for Geometrically Nonconforming Substructures and Discontinuous Coefficients
نویسندگان
چکیده
1 Department of Mathematics, Warsaw University, Warsaw 02-097, Poland. This work was supported in part by The Polish Sciences Foundation under grant NN201006933. 2 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA 3 Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro 22460-320, Brazil 4 Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA
منابع مشابه
Neumann-neumann Methods for a Dg Discretization of Elliptic Problems with Discontinuous Coefficients on Geometrically Nonconforming Substructures
A discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest Ω is assumed to be a union of polygonal substructures Ωi of size O(Hi). We allow this substructure decomposition to be geometrically nonconforming. Inside each substructure Ωi, a conforming finite element space associated to a triangulation Thi...
متن کاملA Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media
In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...
متن کاملAdditive Average Schwarz Methods for Discretization of Elliptic Problems with Highly Discontinuous Coefficients
A second order elliptic problem with highly discontinuous coefficients has been considered. The problem is discretized by two methods: 1) continuous finite element method (FEM) and 2) composite discretization given by a continuous FEM inside the substructures and a discontinuous Galerkin method (DG) across the boundaries of these substructures. The main goal of this paper is to design and analy...
متن کاملAdditive Schwarz Methods for DG Discretization of Elliptic Problems with Discontinuous Coefficient
In this paper we consider a second order elliptic problem defined on a polygonal region Ω, where the diffusion coefficient is a discontinuous function. The problem is discretized by a symmetric interior penalty discontinuous Galerkin (DG) finite element method with triangular elements and piecewise linear functions. Our goal is to design and analyze an additive Schwarz method (ASM), see the boo...
متن کاملAdditive Schwarz Method for DG Discretization of Anisotropic Elliptic Problems
In the paper we consider a second order elliptic problem with discontinuous anisotropic coefficients defined on a polygonal region Ω . The problem is discretized by a Discontinuous Galerkin (DG) finite element method with triangular elements and piecewise linear functions. Our goal is to design and analyze an additive Schwarz method (ASM), see the book by Toselli and Widlund [4], for solving th...
متن کامل