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New Cartesian grid methods for interface problems using the finite element formulation

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Summary

New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients. The triangulations in these methods do not need to fit the interfaces. The basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately. Both non-conforming and conforming finite element spaces are considered. Corresponding interpolation functions are proved to be second order accurate in the maximum norm. The conforming finite element method has been shown to be convergent. With Cartesian triangulations, these new methods can be used as finite difference methods. Numerical examples are provided to support the methods and the theoretical analysis.

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Authors and Affiliations

  1. Center For Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

    Zhilin Li

  2. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

    Tao Lin

  3. Exxon Production Research Company, Applied Mathematics, Caltech, Pasadena, Houston, CA, TX, 91125, USA

    Xiaohui Wu

Authors
  1. Zhilin Li
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  2. Tao Lin
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  3. Xiaohui Wu
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Correspondence to Zhilin Li.

Additional information

Mathematics Subject Classification (2000): 65L10, 65L60, 65L70

In this research, Zhilin Li is supported in part by USA ARO grants, 39676-MA and 43751-MA, USA NSF grants DMS-0073403 and DMS-0201094; USA North Carolina State University FR&PD grant; Tao Lin is supported in part a USA NSF grant DMS-97-04621. Special thanks to Thomas Hou for his participation and contribution to this project. We are also grateful to R. LeVeque, K. Bube, and T. Chan for useful discussions.

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Li, Z., Lin, T. & Wu, X. New Cartesian grid methods for interface problems using the finite element formulation. Numer. Math. 96, 61–98 (2003). https://doi.org/10.1007/s00211-003-0473-x

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  • DOI: https://doi.org/10.1007/s00211-003-0473-x

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