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Superconvergence of finite volume methods for the second-order elliptic problem. (English) Zbl 1173.65354
Summary: This paper derives a superconvergence result for finite volume approximations of the second order elliptic problem by using a \(L^{2}\) projection post-processing technique. The superconvergence result is applicable to different kind of finite volume methods and to general quasi-uniform meshes.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin 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
76D07 Stokes and related (Oseen, etc.) flows
35B45 A priori estimates in context of PDEs
35J50 Variational methods for elliptic systems
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