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

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 ε (1,2]. In 2d, we infer an optimal algebraic convergence rate. In any space dimension d, we achieve the same result for p > 2 d/(d + 2). We also prove convergence without algebraic rates for exact solutions only belonging to the energy space.