Numerical approximations of singular source terms in differential equations

Journal of Computational Physics

Volumn 200, Issue 2, 2004, Pages 462-488

  Tornberg, Anna Karin ^a   Engquist, Björn ^b  

^a NEW YORK UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS;

HIGH-ORDER; HIGHER-ORDER; MULTI DIMENSIONS; NEW HIGH; NUMERICAL APPROXIMATIONS; ONE-DIMENSIONAL PROBLEM; REGULAR GRIDS; REGULARISATION; SINGULAR SOURCES; SOURCE TERMS;

DIFFERENTIAL EQUATIONS;

EID: 7244250225     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.04.011     Document Type: Article

References (18)

1. Beale J.T. Majda A. Vortex methods II: Higher order accuracy in two and three dimensions Math. Comput. 39 1982 29-52
2. Beyer R.P. LeVeque R.J. Analysis of a one-dimensional model for the immersed boundary method SIAM J. Num. Anal. 29 1992 332-364
3. Chorin A.J. Numerical study of slightly viscous flow J. Fluid Mech. 57 1973 785-796
4. Juric D. Tryggvason G. A front-tracking method for dendritic solidification J. Comput. Phys. 123 1996 127-148
5. Kreiss H.O. Thomée V. Widlund O. Smoothing of initial data and rates of convergence for parabolic difference equations Commun. Pur. Appl. Math. 23 1970 241-259
6. G. Ledfelt, A thin wire sub cell model for arbitrary oriented wires for the fd-td method, in: G. Kristensson (Ed.), Proceedings of the EMB 98 - Electromagnetic Computations for Analysis and Design of Complex Systems, 1998, 148-155
7. LeVeque R.J. Li Z.L. Immersed interface methods for stokes flow with elastic boundaries or surface tension SIAM J. Sci. Comput. 18 1997 709-735
8. Monaghan J.J. Extrapolating B splines for interpolation J. Comput. Phys. 60 1985 253-262
9. Osher S.J. Fedkiw R.P. Level Set Methods and Dynamic Implicit Surfaces 2002 Springer Verlag Berlin
10. Peskin C.S. Numerical analysis of blood flow in the heart J. Comput. Phys. 25 1977 220-252
11. Peskin C.S. The immersed boundary method Acta Numer. 11 2002 479-517
12. Raviart P.A. An analysis of particle methods Lecture Notes In Mathematics 1985 253-262 Springer Verlag Berlin
13. Sethian J.A. Level Set Methods and Fast Marching Methods. Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science 1999 Cambridge University Press Cambridge
14. Tornberg A.K. Multi-dimensional quadrature of singular and discontinuous functions BIT 42 2002 644-669
15. Tornberg A.K. Engquist B. Regularization techniques for numerical approximation of PDEs with singularities J. Sci. Comput. 19 2003 527-552
16. Tornberg A.K. Engquist B. The segment projection method for interface tracking Commun. Pur. Appl. Math. 56 2003 47-79
17. Tryggvason G. Bunner B. Esmaeeli A. Juric D. Al-Rawahi N. Tauber W. Han J. Nas S. Jan Y.J. A front-tracking method for the computations of multiphase flow J. Comput. Phys. 169 2001 708-759
18. Waldén J. On the approximation of singular source terms in differential equations Numer. Meth. Part D E 15 1999 503-520