An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems

In this paper we propose a method for the finite element solution of elliptic interface problem, using an approach due to Nitsche. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We show that optimal order of convergence holds without restr...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2002-01, Vol.191 (47), p.5537-5552
Main Authors: Hansbo, Anita, Hansbo, Peter
Format: Article
Language:English
Subjects:
Approximation theory
Computational methods
Computational techniques
Convergence of numerical methods
Discontinuities
Errors
Exact sciences and technology
Finite element method
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Heat conduction
Heat transfer
MATEMATIK
Mathematical methods in physics
MATHEMATICS
Physics
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Summary:In this paper we propose a method for the finite element solution of elliptic interface problem, using an approach due to Nitsche. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. Further, we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples.
ISSN:0045-7825
1879-2138
1879-2138
DOI:10.1016/S0045-7825(02)00524-8