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On multi-parameter error expansions in finite difference methods for linear Dirichlet problems. (English) Zbl 0629.65109

The Dirichlet problem is considered for a second order selfadjoint elliptic partial differential equation in a smooth domain \(\Omega\) in \(R^ n\). A grid is introduced, which is uniform in each coordinate direction. In the interior of \(\Omega\) the differential operator is approximated by the central difference scheme, and near the boundary one- sided differences are used. It is shown that the error may be approximated by a polynomial in the mesh sizes.
Reviewer: G.Hedstrom

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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References:

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