Superconvergence of the gradient of Galerkin approximations for elliptic problems. (English) Zbl 0642.65072
A finite element method for the Dirichlet problem on a square for the equation \(-\Delta u+bu=f\) (b\(\geq 0)\) is considered. It is based on using tensor products of continuous piecewise polynomial spaces. The author shows that a superconvergence phenomenon for the averaged gradient occurs only in case of odd degree polynomials. Numerical examples are given as well.
Reviewer: E.D’yakonov
MSC:
| 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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