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An interior estimate of superconvergence for finite element solutions for second-order elliptic problems on quasi-uniform meshes by local projections. (English) Zbl 1058.65118
The main goal of this paper is to derive some local superconvergence error estimates for the projection method in which \(L^2\) projection is defined locally on subdomains. The results require the exact solution to be only locally smooth. The superconvergence error estimates in \(L^\infty\) are also derived.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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