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An adaptive finite element method for linear elliptic problems. (English) Zbl 0644.65080
A practical adaptive finite element method is developed for a Poisson equation with Dirichlet or Neumann boundary conditions when the exact solution contains a singularity dependent on \(r^{\beta}\) where \(\beta\) lies between 1 and 2 and where r is the distance from the singularity. Criteria are developed for estimating the error in the solution and gradient and techniques given for minimal refinements of the mesh based on the local error estimates. Two numerical examples are given for sectors with internal angles \(3\pi\) /4 and \(\pi\).
Reviewer: K.E.Barrett

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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