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Adaptive discontinuous Galerkin approximations to fourth order parabolic problems


Authors: Emmanuil H. Georgoulis and Juha M. Virtanen
Journal: Math. Comp. 84 (2015), 2163-2190
MSC (2010): Primary 65M15, 65M50, 65M60
DOI: https://doi.org/10.1090/mcom/2936
Published electronically: February 24, 2015
MathSciNet review: 3356023
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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, by resulting in substantial reduction of computational effort.


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Additional Information

Emmanuil H. Georgoulis
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom.
Email: Emmanuil.Georgoulis@le.ac.uk

Juha M. Virtanen
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
Email: jv77@le.ac.uk

DOI: https://doi.org/10.1090/mcom/2936
Received by editor(s): March 7, 2013
Received by editor(s) in revised form: October 28, 2013
Published electronically: February 24, 2015
Article copyright: © Copyright 2015 American Mathematical Society