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Stability and error analysis on partially implicit schemes. (English) Zbl 1076.65079

The author uses an exact error propagation and a discrete scheme smoothing approach to give a posteriori stability and error analysis for a parabolic problem.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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References:

[1] and On an efficient parallel algorithm for solving time dependent partial differential equations, Proceedings of the 1998 International Conference on Parallel and Distributed Processing Technology and Applications, H. R. Arabnia, editor, CSREA Press, Athens, GA, 1998, pp. 357-372.
[2] Galerkin finite element methods for parabolic problems, Springer, New York, 1997. · Zbl 0884.65097 · doi:10.1007/978-3-662-03359-3
[3] Numerical analysis of semilinear parabolic problems, The Graduate Student’s Guide to Numerical Analysis ’98, and editors, SSCM Vol. 26, Springer-Verlag, 1999, pp. 83-117.
[4] Sun, Applications & Algorithms 9 pp 115– (2002)
[5] Sun, J Comput Appl Math
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