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Superconvergence and extrapolation of the bilinear finite element method for nonsymmetric and indefinite problems. (Chinese. English summary) Zbl 1289.65248

Summary: The bilinear finite element method is discussed to approximate nonsymmetric and indefinite problems. Applying the interpolation of the elements instead of Ritz projection, and with the help of the known high accuracy analysis and averaging technique, the superclose property and global superconvergence result with \(O(h^2)\) order are obtained in \(H^1\)-norm. Furthermore, two new high asymptotic error expansions are deduced and the extrapolation solution with \(O(h^3)\) order is derived which is two order higher than the traditional error estimate.

MSC:

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
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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