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Convergence of adaptive finite element methods. (English) Zbl 1016.65074
The authors consider the use of adaptive finite element methods. They construct an algorithm, which converges linearly and which does not involve preliminary mesh adaptation. They give the results of a number of numerical experiments and point out the possibilities associated with higher order elements and saddle point problems are also discussed. The theory is illustrated a number of diagrams.

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
65Y20 Complexity and performance of numerical algorithms
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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