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Improved accuracy by adapted mesh-refinements in the finite element method. (English) Zbl 0571.65097

The paper deals with a finite element approximation to the Green function of the Neumann problem for a second order elliptic equation. Optimal order error estimates are proved for this problem using the finite element spaces on refined meshes, adapted to the known singularity of the solution. These estimates (for the solution and its gradient) are derived in \(L_ 1\)-norm, and an improved pointwise convergence is also shown near the singularity.
Reviewer: D.Fagé

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
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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