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An adaptive finite element method with efficient maximum norm error control for elliptic problems. (English) Zbl 0806.65106

Author’s summary: A posteriori and a priori error estimates are derived for a finite element discretization method applied to an elliptic model problem. The underlying partitions need not be quasi-uniform and can be highly graded; only a certain weak, local mesh regularity is assumed. The error is bounded in terms of the local mesh size and the local regularity of the solution and data. An adaptive algorithm is designed for automatic control of the discretization error in the maximum norm. The error control is proved to be both reliable and efficient.

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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