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

Daniele Antonio Di Pietro (1) , Alexandre Ern (2)

1 IFPEN - IFP Energies nouvelles
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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.

Domaines: Analyse numérique [math.NA]

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⟩