Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions - Archive ouverte HAL Access content directly
Journal Articles Numerical Methods for Partial Differential Equations Year : 2011

Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions

Abstract

We study the convergence of the Symmetric Weighted Interior Penalty discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions only belonging to $W^{2,p}$ with $p\in(1,2]$. In 2d we infer an optimal algebraic convergence rate. In 3d we achieve the same result for $p>\nicefrac65$ , and for $p\in(1,\nicefrac65]$ we prove convergence without algebraic rate.
Fichier principal
Vignette du fichier
W2p.pdf (743.71 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00514387 , version 1 (02-09-2010)

Identifiers

Cite

Daniele Antonio Di Pietro, Alexandre Ern. Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions. Numerical Methods for Partial Differential Equations, 2011, 17 p. ⟨10.1002/num.20675⟩. ⟨hal-00514387⟩
162 View
230 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More