Superconvergence of solution derivatives for the Shortley-Weller difference approximation of Poisson’s equation. II: Sigularity problems. (English) Zbl 1031.65118
This is a continued analysis on superconvergence of solution derivatives for the Shortley-Weller approximation in part I by Z. C. Li, T. Yamamoto, and Q. Fang [J. Comput. Appl. Math. 151, 307-333 (2003; Zbl 1030.65112)], which is to explore superconvergence for unbounded derivatives near the boundary. By using the stretching function the second order superconvergence for the solution derivatives is established. Moreover, numerical experiments are provided to support the error analysis made.
The analytical approaches in this article are non-trivial and intriguing. This article also provides the superconvergence analysis for the bilinear finite element method and the finite difference method with nine nodes.
The analytical approaches in this article are non-trivial and intriguing. This article also provides the superconvergence analysis for the bilinear finite element method and the finite difference method with nine nodes.
Reviewer: Leonid B.Chubarov (Novosibirsk)
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
Shortley-Weller approximation; finite element method; finite difference method; Poisson’s equation; stretching function; error analysis; superconvergence; numerical experimentsCitations:
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