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


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
Full Text: EuDML


[1] Г. И. Марчук В. В. Шайдуров: Повышение точности решений разностных схем. Москва, Наука, 1979. · Zbl 1225.01075
[2] О. А. Ладыженская Н. Н. Уралъцева: Линейные и квазилинейные уравнения эллиптического типа. Москва, Наука, 1973. · Zbl 1221.53041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.