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A regularized correction method for elliptic problems with a singular force

김혜현
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회지 (Journal of the KMS)|제49권 제5호|pp. 927-945

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참고문헌

키워드

Dirac delta functionsecond order methodsimmersed boundary
주제분류수학

초록

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

Abstract

An approximation of singular source terms in elliptic problems is developed and analyzed. Under certain assumptions on the curve where the singular source is defined, the second order convergence in the maximum norm can be proved. Numerical results present its better performance compared to previously developed regularization techniques.

참고문헌 (12)

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  4. E. Givelberg, "Immersed finite element method", ~
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  6. A. Mayo, "The fast solution of Poisson's and the biharmonic equations on irregular regions", SIAM J. Numer. Anal, 21(2), pp.285~299 (1984)
  7. A. Mayo, "Fast high order accurate solution of Laplace's equation on irregular regions", SIAM J. Sci. Statist. Comput, 6(1), pp.144~157 (1985)
  8. C. S. Peskin, "Numerical analysis of blood ow in the heart", J. Computational Phys, 25(3), pp.220~252 (1977)
  9. C. S. Peskin, "The immersed boundary method", Acta Numer, 11, pp.479~517 (2002)
  10. A.-K. Tornberg, "Numerical approximations of singular source terms in differential equations", J. Comput. Phys, 200(2), pp.462~488 (2004)
  11. A.-K. Tornberg, "Regularization techniques for numerical approximation of PDEs with singular- ities", J. Sci. Comput, 19(1), pp.527~552 (2003)
  12. L. Zhang, "Immersed finite element method", Comput. Methods Appl. Mech. Engrg, 193(21), pp.2051~2067 (2004)

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