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

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.

Dmitry Kolomenskiy, Romain Nguyen van Yen, Kai Schneider. Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions. Applied Numerical Analysis and Computational Mathematics, Wiley-VCH Verlag: No OnlineOpen, 2015, 95, pp.238-249. ⟨10.1016/j.apnum.2014.02.003⟩. ⟨hal-01299247⟩

Journal: Applied Numerical Analysis and Computational Mathematics

Date de publication: 01-09-2015

Auteurs:
  • Dmitry Kolomenskiy
  • Romain Nguyen van Yen
  • Kai Schneider

Digital object identifier (doi): http://dx.doi.org/10.1016/j.apnum.2014.02.003

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