Interior penalty discontinuous Galerkin methods with implicit time-integration techniques for nonlinear parabolic equations

Abstract

We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkinscheme with the implicit -schemes in time, which include backward Euler and CrankNicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. (c) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013