A discontinuous Galerkin method for elliptic interface problems with application to electroporation

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We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L(2)-norm. We apply our method to the numerical Study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright (C) 2008 John Wiley & Sons, Ltd.
Publisher
JOHN WILEY & SONS LTD
Issue Date
2009-10
Language
English
Article Type
Article
Citation

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, v.25, pp.991 - 1008

ISSN
1069-8299
DOI
10.1002/cnm.1132
URI
http://hdl.handle.net/10203/95242
Appears in Collection
MA-Journal Papers(저널논문)
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