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

2017/02/19 by Li, Buyang · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1702.05696

Abstract

In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the L^q norm, 1≤ q≤∞, 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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