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Monotone and conservative difference schemes for elliptic equations with mixed derivatives. (English) Zbl 1081.65098

A new difference scheme for elliptic boundary value problems in the plane with mixed derivatives and alternating coefficients is presented. It is shown that this scheme is conservative, has the second order of approximation and satisfies the grid maximum principle. A priori estimates of stability and convergence in the uniform norm are also obtained.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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