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Convergence analysis in the maximum norm of the numerical gradient of the Shortley-Weller method. (English) Zbl 1397.65227

The authors consider the well-known Shortley-Weller finite difference approximation (known to be of second order) of the Dirichlet problem to the Poisson equation in dimensions 2 and 3. Assuming up to 5 continuous derivatives of the exact solution and using the maximum and a discrete commutativity principle, they show a super-convergence result: the central difference quotients give a second-order approximation to the components of the gradient at the positions of the staggered grid.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
30B50 Dirichlet series, exponential series and other series in one complex variable
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