Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions

Dmitriy Leykekhman, Buyang Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

Abstract

As a model of the second order elliptic equation with non-trivial boundary conditions, we consider the Laplace equation with mixed Dirichlet and Neumann boundary conditions on convex polygonal domains. Our goal is to establish that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon–Miranda) discrete maximum principle, and then prove the stability of the Ritz projection with mixed boundary conditions in L∞norm. Such results have a number of applications, but are not available in the literature. Our proof of the maximum-norm stability of the Ritz projection is based on converting the mixed boundary value problem to a pure Neumann problem, which is of independent interest.
Original languageEnglish
Pages (from-to)541-565
Number of pages25
JournalCalcolo
Volume54
Issue number2
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Finite element method
  • Maximum norm
  • Stability

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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