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http://dx.doi.org/10.4134/JKMS.2012.49.5.927

A REGULARIZED CORRECTION METHOD FOR ELLIPTIC PROBLEMS WITH A SINGULAR FORCE  

Kim, Hyea-Hyun (Department of Applied Mathematics Kyung Hee University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 927-945 More about this Journal
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.
Keywords
Dirac delta function; second order methods; immersed boundary;
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1 D. Boffi and L. Gastaldi, A nite element approach for the immersed boundary method, Comput. & Structures 81 (2003), no. 8-11, 491-501.   DOI   ScienceOn
2 D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001.
3 E. Givelberg, Immersed nite element method, Preprint.
4 R. J. LeVeque and Z. L. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994), no. 4, 1019-1044.   DOI   ScienceOn
5 A. Mayo, The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM J. Numer. Anal. 21 (1984), no. 2, 285-299.   DOI   ScienceOn
6 A. Mayo, Fast high order accurate solution of Laplace's equation on irregular regions, SIAM J. Sci. Statist. Comput. 6 (1985), no. 1, 144-157.   DOI
7 C. S. Peskin, Numerical analysis of blood ow in the heart, J. Computational Phys. 25 (1977), no. 3, 220-252.   DOI   ScienceOn
8 C. S. Peskin, The immersed boundary method, Acta Numer. 11 (2002), 479-517.   DOI
9 A.-K. Tornberg and B. Engquist, Numerical approximations of singular source terms in differential equations, J. Comput. Phys. 200 (2004), no. 2, 462-488.   DOI   ScienceOn
10 A.-K. Tornberg and B. Engquist, Regularization techniques for numerical approximation of PDEs with singularities, J. Sci. Comput. 19 (2003), no. 1-3, 527-552.   DOI
11 L. Zhang, A. Gerstenberger, X. Wang, and W. K. Liu, Immersed nite element method, Comput. Methods Appl. Mech. Engrg. 193 (2004), no. 21-22, 2051-2067,   DOI   ScienceOn
12 J. T. Beale and A. T. Layton, On the accuracy of nite difference methods for elliptic problems with interfaces, Commun. Appl. Math. Comput. Sci. 1 (2006), 91-119.   DOI