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multi-parameter asymptotic error expansion; Richardson extrapolations; Dirichlet problem; deferred corrections; improving the accuracy
The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.
[1] V. Pereyra W. Proskurowski O. Widlund: High order fast Laplace solvers for Dirichlet problem on general domains. Math. Соmр. 31, 137 (1977), 1 - 17. MR 0431736
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