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.
Reviewer: Laura-Iulia Aniţa (Iaşi)
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 |
