A new formulation for imposing Dirichlet boundary conditions on non-matching meshes

Aurelia Cuba Ramos, Alejandro M. Aragón, Soheil Soghrati, Philippe H. Geubelle, Jean François Molinari

Research output: Contribution to journalArticlepeer-review

Abstract

Generating matching meshes for problems with complex boundaries is often an intricate process, and the use of non-matching meshes appears as an appealing solution. Yet, enforcing boundary conditions on non-matching meshes is not a straightforward process, especially when prescribing those of Dirichlet type. By combining a type of Generalized Finite Element Method (GFEM) with the Lagrange multiplier method, a new technique for the treatment of essential boundary conditions on non-matching meshes is introduced in this manuscript. The new formulation yields a symmetric stiffness matrix and is straightforward to implement. As a result, the methodology makes possible the analysis of problems with the use of simple structured meshes, irrespective of the problem domain boundary. Through the solution of linear elastic problems, we show that the optimal rate of convergence is preserved for piecewise linear finite elements. Yet, the formulation is general and thus it can be extended to other elliptic boundary value problems.

Original languageEnglish (US)
Pages (from-to)430-444
Number of pages15
JournalInternational Journal for Numerical Methods in Engineering
Volume103
Issue number6
DOIs
StatePublished - Aug 10 2015

Keywords

  • Dirichlet boundary conditions
  • GFEM
  • IGFEM
  • Lagrange multiplier method
  • Non-matching meshes
  • XFEM

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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