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Higher-order compact mixed methods. (English) Zbl 0885.65109
The authors construct a class of mixed higher-order finite difference schemes on compact stencils for second-order elliptic partial differential equations. Dirichlet and Neumann boundary conditions for the 2D problem are considered. The resulting difference solutions are \(O(h^4)\) accurate in both \(u\) and the flux \(\sigma= \nabla u\) at the grid points, where \(u\) is the solution of the corresponding boundary value problem. The results of some numerical experiments are presented to demonstrate the superconvergence rates.
Reviewer: V.Makarov (Kyïv)

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
35J25 Boundary value problems for second-order elliptic equations
Software:
MUDPACK-2; MUDPACK
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References:
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