Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

Georgoulis, Emmanuil; Virtanen, Juha

doi:10.1090/mcom/2936

Adaptive discontinuous Galerkin approximations to fourth order parabolic problems
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Math. Comp. 84 (2015), 2163-2190 Request permission

Abstract:

An adaptive algorithm, based on residual type a posteriori indicators of errors measured in $L^\infty (L^2)$ and $L^2(L^2)$ 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 $r \ge 2$. 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.

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