Journal
APPLIED NUMERICAL MATHEMATICS
Volume 95, Issue -, Pages 238-249Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2014.02.003
Keywords
Volume penalization; Neumann boundary conditions; Laplace operator; Poisson equation
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Funding
- Humboldt Foundation
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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. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
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