Analyticity, Maximal Regularity and Maximum-norm Stability of Semi-Discrete Finite Element Solutions of Parabolic Equations in Nonconvex Polyhedra

Buyang Li

doi:10.1090/mcom/3316

Analyticity, Maximal Regularity and Maximum-norm Stability of Semi-Discrete Finite Element Solutions of Parabolic Equations in Nonconvex Polyhedra

Buyang Li

Research output: Journal article publication › Journal article › Academic research › peer-review

14 Citations (Scopus)

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 Lp-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 maximumnorm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.

Original language	English
Pages (from-to)	1-44
Number of pages	44
Journal	Mathematics of Computation
Volume	88
Issue number	315
DOIs	https://doi.org/10.1090/mcom/3316
Publication status	Published - 2018

Keywords

Analytic semigroup
Finite element method
Maximal L-regularity
Maximum-norm stability
Nonconvex polyhedra
Parabolic equation

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

More information

10.1090/mcom/3316

http://hdl.handle.net/10397/92485

Cite this

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AB - In general polygons and polyhedra, possibly nonconvex, the analyticity of the finite element heat semigroup in the Lq-norm, 1 ≤ q ≤ ∞, and the maximal Lp-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 maximumnorm stability of the Ritz projection, which currently is known to hold for general polygonal domains and convex polyhedral domains.

KW - Analytic semigroup

KW - Finite element method

KW - Maximal L-regularity

KW - Maximum-norm stability

KW - Nonconvex polyhedra

KW - Parabolic equation

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JF - Mathematics of Computation

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ER -

Analyticity, Maximal Regularity and Maximum-norm Stability of Semi-Discrete Finite Element Solutions of Parabolic Equations in Nonconvex Polyhedra

Abstract

Keywords

ASJC Scopus subject areas

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