Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

Abstract. An adaptive algorithm, based on residual type a posteriori indicators of errors measured in L∞(L2) and L2(L2) norms, for a numerical scheme consisting of implicit Euler method in time and discontinuous Galerkin method in space for linear parabolic fourth order problems is presented. The a posteriori analysis is performed for convex domains in two and three space dimensions for local spatial polynomial degrees r ≥ 2. The a posteriori estimates are then used within an adaptive algorithm, highlighting their relevance in practical computations, by resulting in substantial reduction of computational effort.