Weak discrete maximum principle of finite element methods in convex polyhedra

Dmitriy Leykekhman; Buyang Li

doi:10.1090/mcom/3560

Weak discrete maximum principle of finite element methods in convex polyhedra

Dmitriy Leykekhman, Buyang Li

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

2 Citations (Scopus)

Abstract

We prove that the Galerkin finite element solution uh of the Laplace equation in a convex polyhedron Ω, with a quasi-uniform tetrahedral partition of the domain and with finite elements of polynomial degree r 1, satisfies the following weak maximum principle:

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Mathematics of Computation
Volume	90
Issue number	327
DOIs	https://doi.org/10.1090/mcom/3560
Publication status	Published - Jan 2021

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

More information

10.1090/mcom/3560

http://hdl.handle.net/10397/89361

Cite this

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title = "Weak discrete maximum principle of finite element methods in convex polyhedra",

abstract = "We prove that the Galerkin finite element solution uh of the Laplace equation in a convex polyhedron Ω, with a quasi-uniform tetrahedral partition of the domain and with finite elements of polynomial degree r 1, satisfies the following weak maximum principle:",

author = "Dmitriy Leykekhman and Buyang Li",

note = "Funding Information: Received by the editor September 18, 2019, and, in revised form, February 29, 2020, and April 13, 2020. 2010 Mathematics Subject Classification. Primary 65N12, 65N30. This work was partially supported by NSF DMS-1913133 and a Hong Kong RGC grant (project no. 15300519). Publisher Copyright: {\textcopyright} 2021. All Rights Reserved.",

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AU - Li, Buyang

N1 - Funding Information: Received by the editor September 18, 2019, and, in revised form, February 29, 2020, and April 13, 2020. 2010 Mathematics Subject Classification. Primary 65N12, 65N30. This work was partially supported by NSF DMS-1913133 and a Hong Kong RGC grant (project no. 15300519). Publisher Copyright: © 2021. All Rights Reserved.

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N2 - We prove that the Galerkin finite element solution uh of the Laplace equation in a convex polyhedron Ω, with a quasi-uniform tetrahedral partition of the domain and with finite elements of polynomial degree r 1, satisfies the following weak maximum principle:

AB - We prove that the Galerkin finite element solution uh of the Laplace equation in a convex polyhedron Ω, with a quasi-uniform tetrahedral partition of the domain and with finite elements of polynomial degree r 1, satisfies the following weak maximum principle:

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Weak discrete maximum principle of finite element methods in convex polyhedra

Abstract

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