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On an h-type mesh-refinement strategy based on minimization of interpolation errors. (English) Zbl 0556.73081

An adaptive finite element method is proposed which involves an automatic mesh refinement in areas of the mesh where local errors are determined to exceed a pre-assigned limit. The estimation of local errors is based on interpolation error bounds and extraction formulas for highly accurate estimates of second derivatives. Applications to several two-dimensional model problems are discussed. The results indicate that the method can be very effective for both regular problems and problems with strong singularities.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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References:

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