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On the convergence of boundary element methods for initial-Neumann problems for the heat equation
Author(s):
Yang
Hongtao.
Journal:
Math. Comp.
68
(1999),
547-557.
MSC (1991):
Primary 65M30;
Secondary 65R20
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Abstract:
In this paper we study boundary element methods for initial-Neumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.
References:
- 1.
- D.N. Arnold and P.J. Noon, Coercivity of the single layer heat potential, J. Comp. Math. 8 (1989), 1-7. MR 90k:65186
- 2.
- D. N. Arnold and W.L. Wendland, On the asymptotic convergence of collocation methods, Math. Comp. 44 (1983), 349-381. MR 85h:65254
- 3.
- C.T.H. Baker, The Treatment of Integral Equations, Clarendon Press, 1977. MR 57:7079
- 4.
- C.A. Brebbia and D. Nardin, Solution of parabolic and hyperbolic time dependent problems using boundary elements, Comp. & Maths with Aplls. 12b (1986), 1061-1072. MR 88f:65218
- 5.
- C.A. Brebbia and L.A. Wrobel, The solution of parabolic problems using the dual reciprocity boundary element, Advanced Boundary Element Methods (ed. by P.K. Cruse). MR 89b:65226
- 6.
- M. Costabel, Boundary integral operators for the heat equation, Integral Equation and Operator Theory 13 (1990), 498-552. MR 91j:35119
- 7.
- M. Costabel, K. Onishi and W.L. Wendland, A boundary element collocation method for the Neumann problem of the heat equation, Inverse and Ill-Posed Problems, Academic Press, Inc., 1987, pp. 369-384. MR 90k:65177
- 8.
- D. Curran and B.A. Lewis, Boundary element method for the solution of the transient diffusion equation in two dimensions, Appl. Math. Modeling 10 (1986), 107-113.
- 9.
- F. De Hoog and R. Weiss, On the solution of a Volterra integral equation with a weakly singular kernel, SIAM J. Math.Anal. 4 (1973), 561-573. MR 49:1818
- 10.
- A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, 1964. MR 31:6062
- 11.
- Huang Mingyou, Finite Element Methods for Evolution Equations, Shanghai Press of Technology and Science, 1983.
- 12.
- Li Ronghua and Feng Guocheng, The Numerical Treatment for Differential Equations, The People's Education Press, 1980.
- 13.
- P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM Philadelphia, 1985. MR 86m:65163
- 14.
- J.L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vols. 1-2, Springer-Verlag, 1973. MR 50:2670; MR 50:2671
- 15.
- E.A. McIntyre, Jr., Boundary integral solutions for the heat equation, Math. Comp. 46 (1986), 71-79. MR 87h:65214
- 16.
- J.C. Nedelec, Curved finite element methods for the solution of integral singular equation in
, Comput. Methods Appl. Mech. Engrg. 8 (1976), 61-80. MR 56:13741 - 17.
- P.J. Noon, The single layer heat potential and Galerkin boundary element methods for the heat equation, Ph.D. thesis, University of Maryland, U.S.A., 1988
- 18.
- K. Onishi, Convergence in the boundary element method for heat equation, TRU Mathematics (Science University of Tokyo) 17 (1981), 213-225. MR 83a:65088
- 19.
- K. Onishi, Boundary element method for time dependent heat equation, Proceedings of the 1st Japan-China Symposium on Boundary Element Methods (ed. by M. Takana and Q. Du).
- 20.
- F. Sgallari, A weak formulation of boundary integral equations for time dependent problems, Appl. Math. Modeling 9 (1985), 295-301. MR 86h:65146
- 21.
- Yang Hongtao, A new analysis of Volterra-Fredholm boundary integral equations of the second kind, Northeast. Math. J. 13 (3) (1997), 325-334.
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Additional Information:
Yang
Hongtao
Affiliation:
Department of Mathematics, Jilin University, Changchun, 130023, China
DOI:
10.1090/S0025-5718-99-01022-4
PII:
S 0025-5718(99)01022-4
Keywords:
Heat equation,
boundary element method,
error estimate
Received by editor(s):
January 4, 1994
Received by editor(s) in revised form:
January 26, 1996 and February 18, 1997
Additional Notes:
This work was supported by the National Natural Science Foundation of China.
Copyright of article:
Copyright
1999,
American Mathematical Society
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