On the approximation of singular source terms in differential equations

Numerical Methods for Partial Differential Equations

Volumn 15, Issue 4, 1999, Pages 503-520

  Waldén, Johan ^a,b  

^a UPPSALA UNIVERSITY   (Sweden)

^b YALE UNIVERSITY   (United States)

Author keywords

Discrete delta functions; Numerical analysis; Singular source terms

Indexed keywords

EID: 0039523559     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199907)15:4<503::AID-NUM6>3.0.CO;2-Q     Document Type: Article

References (12)

1. H. O. Kreiss, Difference approximations for boundary and eigenvalue problems for ordinary differential equations, Math Comp 26 (1972), 605-624.
2. V. Thomée, Convergence estimates for semi-discrete Galerkin methods for initial-value problems, Tech Rep 26, Chalmers Inst Tech, Sweden, 1972.
3. V. Thomée and B. Wendroff, Convergence estimates for Galerkin methods for variable coefficients initial-value problems, SIAM J Numer Anal 11 (1974), 1059-1068.
4. A. Zemla, On the fundamental solutions for the difference Helmholtz operator, SIAM J Numer Anal 32 (1995), 560-570.
5. R. Glowinski, T. W. Pan, R. O. Wells Jr., and X. Zhou, Wavelet and finite element solutions for the Neumann problem using fictitious domains, Rice Univ, Preprint, 1995.
6. C. S. Peskin, Numerical analysis of blood flow in the heart, J Comp Phys 25 (1977), 220-252.
7. R. P. Beyer and R. J. Leveque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J Numer Anal 29 (1992), 332-364.
8. R. P. Beyer, A computational model of the cochlea using the immersed boundary method, J Comp Phys 98 (1992), 145-162.
9. R. J. Leveque and Z. Li, Immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J Numer Anal 31 (1994), 1019-1044.
10. G. Beylkin, On the fast Fourier transform of functions with singularities, Appl Comp Harmon Anal 2 (1995), 363-381.
11. G. Fix and G. Strang, "A Fourier analysis of the finite element variational method," Constructive aspects of functional analysis, Rome, 1973.
12. C. K. Chui, An introduction to wavelets, Academic Press, New York, 1992.