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arXiv · 1303.2524

Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

Emmanuil H. Georgoulis·Juha M. Virtanen
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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, which results into substantial reduction of computational effort.

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Emmanuil H. Georgoulis, Juha M. Virtanen. 2013-03-11. Adaptive discontinuous Galerkin approximations to fourth order parabolic problems. https://arxiv.org/abs/1303.2524

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