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Discontinuous Galerkin methods for periodic boundary value problems
Author(s) -
Vemaganti Kumar
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20191
Subject(s) - homogenization (climate) , mathematics , boundary value problem , finite element method , discontinuous galerkin method , galerkin method , partial differential equation , constraint (computer aided design) , extension (predicate logic) , mathematical analysis , partial derivative , geometry , computer science , biodiversity , ecology , physics , biology , programming language , thermodynamics
This article considers the extension of well‐known discontinuous Galerkin (DG) finite element formulations to elliptic problems with periodic boundary conditions. Such problems routinely appear in a number of applications, particularly in homogenization of composite materials. We propose an approach in which the periodicity constraint is incorporated weakly in the variational formulation of the problem. Both H 1 and L 2 error estimates are presented. A numerical example confirming theoretical estimates is shown. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007