Galerkin methods for singular boundary value problems in one space dimension

Eriksson, Kenneth; Thomée, Vidar

doi:10.1090/S0025-5718-1984-0736441-1

Galerkin methods for singular boundary value problems in one space dimension
HTML articles powered by AMS MathViewer

by Kenneth Eriksson and Vidar Thomée PDF

Math. Comp. 42 (1984), 345-367 Request permission

Abstract:

Two Galerkin type piecewise polynomial approximation procedures based on bilinear forms with different weight functions are analyzed and compared. Optimal order error estimates are proved and numerical results are presented.

References

D. C. Brabston and H. B. Keller, A numerical method for singular two point boundary value problems, SIAM J. Numer. Anal. 14 (1977), no. 5, 779–791. MR 483475, DOI 10.1137/0714054
Frank R. de Hoog and Richard Weiss, On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind, SIAM J. Math. Anal. 11 (1980), no. 1, 41–60. MR 556495, DOI 10.1137/0511003

Finite Element Methods for Spherically Symmetric Elliptic Equations

Bertil Gustafsson, A numerical method for solving singular boundary value problems, Numer. Math. 21 (1973/74), 328–344. MR 337015, DOI 10.1007/BF01436387
Pierre Jamet, On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems, Numer. Math. 14 (1969/70), 355–378. MR 261799, DOI 10.1007/BF02165591
Dennis Jespersen, Ritz-Galerkin methods for singular boundary value problems, SIAM J. Numer. Anal. 15 (1978), no. 4, 813–834. MR 488786, DOI 10.1137/0715054
R. D. Russell and L. F. Shampine, Numerical methods for singular boundary value problems, SIAM J. Numer. Anal. 12 (1975), 13–36. MR 400723, DOI 10.1137/0712002
Robert Schreiber and Stanley C. Eisenstat, Finite element methods for spherically symmetric elliptic equations, SIAM J. Numer. Anal. 18 (1981), no. 3, 546–558. MR 615530, DOI 10.1137/0718034
Mary Fanett Wheeler, $L_{\infty }$ estimates of optimal orders for Galerkin methods for one-dimensional second order parabolic and hyperbolic equations, SIAM J. Numer. Anal. 10 (1973), 908–913. MR 343658, DOI 10.1137/0710076