Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions

In this paper we derive an a priori error analysis for interior penalty discontinuous Galerkin finite element discretizations of the Poisson equation with exact solution in W2,p, p∈(1,2]. We show that the DGFEM converges at an optimal algebraic rate with respect to the number of degrees of freedom.

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