Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra

Li, Buyang

doi:10.1090/mcom/3316

Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra
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by Buyang Li;

Math. Comp. 88 (2019), 1-44

DOI: https://doi.org/10.1090/mcom/3316

Published electronically: March 19, 2018

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Previous version: Original version posted March 19, 2018
Corrected version: Current version corrects publisher's error which introduced typos into equations at the bottom of page 17 and top of page 18.

Abstract:

In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the $L^q$-norm, $1\leq q\leq \infty$, and the maximal $L^p$-regularity of semi-discrete finite element solutions of parabolic equations are proved. By using these results, the problem of maximum-norm stability of the finite element parabolic projection is reduced to the maximum-norm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.

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