A numerical method for handling boundary and transmission conditions in some linear partial differential equations

Franck Assous, Michael Michaeli

Research output: Contribution to journalConference articlepeer-review

Abstract

In this paper, we propose a method derived from a Nitsche approach for handling boundary and transmission conditions in some partial differential equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. We propose here an extension to vector div -curl problems. Two examples of applications are presented. The first one is concerned with the Maxwell equations. This allows us to solve these equations, particularly in domains with reentrant corners, where the solution can be singular. The second example deals with the Navier-Lame equations. One can handle the case of a crack existence in a plate domain made of several different layers, characterized by different material properties. Numerical experiments are reported.

Original languageEnglish
Pages (from-to)422-431
Number of pages10
JournalProcedia Computer Science
Volume9
DOIs
StatePublished - 2012
Event12th Annual International Conference on Computational Science, ICCS 2012 - Omaha, NB, United States
Duration: 4 Jun 20126 Jun 2012

Keywords

  • Crack tip
  • Elasticity
  • Maxwell equations
  • Nitsche method
  • Singular domains

All Science Journal Classification (ASJC) codes

  • General Computer Science

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