%P 2088-2106
%D 2013
%T Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients
%A I Smears
%A E Sueli
%V 51
%N 4
%X Nondivergence form elliptic equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of these problems which satisfy the Cordès condition. It is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size $h$ and suboptimal with respect to the polynomial degree $p$ by only half an order. Numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under $hp$-refinement for problems with discontinuous coefficients and nonsmooth solutions.
%O This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
%I SIAM PUBLICATIONS
%J SIAM: Journal on Numerical Analysis
%K Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, discontinuous Galerkin, hp-DGFEM, Cordes condition, nondivergence form, discontinuous coefficients, PDEs, finite element methods, CONVERGENCE, VERSION
%L discovery1572511