Numerical verification for elliptic boundary value problem with nonconforming P1 finite elements

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose a numerical method with the nonconforming P1 FEM to verify the existence of solutions to an elliptic boundary value problem. Formulating the boundary value problem as a fixed-point problem on the sum space of the nonconforming P1 finite element space with the Sobolev space of 1st order with zero Dirichlet condition, we construct the numerical verification method based on the Schauder fixed-point theorem. We show a constructive inequality for a boundary integral that appears due to the discontinuity of a nonconforming P1 finite element function. Finally, we present a numerical example to show our proposed method works well.

Original languageEnglish
Title of host publicationScientific Computing, Computer Arithmetic, and Validated Numerics - 16th International Symposium, SCAN 2014, Revised Selected Papers
EditorsJürgen Wolff von Gudenberg, Warwick Tucker, Marco Nehmeier
PublisherSpringer-Verlag
Pages269-279
Number of pages11
ISBN (Print)9783319317687
DOIs
Publication statusPublished - 2016 Jan 1
Externally publishedYes
Event16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014 - Wurzburg, Germany
Duration: 2014 Sep 212014 Sep 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9553
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, SCAN 2014
Country/TerritoryGermany
CityWurzburg
Period14/9/2114/9/26

Keywords

  • Elliptic boundary value problem
  • Nakao’s method
  • Nonconforming P finite element
  • Numerical verification

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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