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A convergent adaptive algorithm for Poisson’s equation. (English) Zbl 0854.65090
The authors develop a convergent adaptive algorithm for linear elements applied to Poisson’s equation in two space dimension. Existence and uniqueness of the problem are illustrated by examples. Extensions are made to higher-order elements in two space dimensions and numerical results are included.

MSC:
65N12 Stability and convergence of numerical 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
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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