Adaptive discontinuous Galerkin approximations to fourth order parabolic problems

2013/03/11 by Emmanuil H. Georgoulis, Georgoulis, Emmanuil H., Juha M. Virtanen +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1303.2524

openalex publication_date 2013/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, which results into substantial reduction of computational effort.

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