## High order fast Laplace solvers for the Dirichlet problem on general regions

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- by Victor Pereyra, Wlodzimierz Proskurowski and Olof Widlund PDF
- Math. Comp.
**31**(1977), 1-16 Request permission

## Abstract:

Highly accurate finite difference schemes are developed for Laplaceâ€™s equation with the Dirichlet boundary condition on general bounded regions in ${R^n}$. A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size*h*, one of the methods has an accuracy of at least $O({h^{5.5}})$ in ${L_2}$. The linear systems of algebraic equations are solved by a capacitance matrix method. The results of our numerical experiments show that highly accurate solutions are obtained with only a slight additional use of computer time when compared to the results obtained by second order accurate methods.

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## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp.
**31**(1977), 1-16 - MSC: Primary 65N15; Secondary 65B05
- DOI: https://doi.org/10.1090/S0025-5718-1977-0431736-X
- MathSciNet review: 0431736