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arXiv · 1804.09065

On $p$-robust saturation on quadrangulations

Jan Westerdiep
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Abstract

For the Poisson problem in two dimensions, posed on a domain partitioned into axis-aligned rectangles with up to one hanging node per edge, we envision an efficient error reduction step in an instance-optimal $hp$-adaptive finite element method. Central to this is the problem: Which increase in local polynomial degree ensures $p$-robust contraction of the error in energy norm? We reduce this problem to a small number of saturation problems on the reference square, and provide strong numerical evidence for their solution.

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Jan Westerdiep. 2018-04-24. On $p$-robust saturation on quadrangulations. https://doi.org/10.1515/cmam-2018-0136

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