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A finite element method for interface problems in domains with smooth boundaries and interfaces

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Abstract

This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite element method to the perturbed problem on the approximate polygonal domains. It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation. As such the method is robust in the regularity of the data in the original problem.

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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, 77843, College Station, TX, USA

    James H. Bramble

  2. Department of Mathematical Sciences, University of Cincinnati, 45221-0025, Cincinnati, OH, USA

    J. Thomas King

Authors
  1. James H. Bramble
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  2. J. Thomas King
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Communicated by D.N. Arnold

This manuscript has been authored under contract number DE-AC02-76CH00016 with the U.S. Department of Energy. Accordingly, the U.S. Government retains a non-exclusive, royalty free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes. This work was also supported in part under National Science Foundation Grant No. DMS-9007185 and by the U.S. Army Research Office through the Mathematical Sciences Institute, Cornell University.

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Bramble, J.H., King, J.T. A finite element method for interface problems in domains with smooth boundaries and interfaces. Adv Comput Math 6, 109–138 (1996). https://doi.org/10.1007/BF02127700

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  • DOI: https://doi.org/10.1007/BF02127700

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