Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions

Dmitry Kolomenskiy, Romain Nguyen Van Yen, Kai Schneider

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretization and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.

Original languageEnglish
Pages (from-to)238-249
Number of pages12
JournalApplied Numerical Mathematics
Volume95
DOIs
Publication statusPublished - 26 May 2015
Externally publishedYes

Keywords

  • Laplace operator
  • Neumann boundary conditions
  • Poisson equation
  • Volume penalization

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