Résumé
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.