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Adaptive finite element strategies based on error assessment. (English) Zbl 0968.74066

Summary: Two main ingredients are needed for adaptive finite element computations. First, the error of a given solution must be assessed by means of either error estimators or error indicators. After that, a new spatial discretization must be defined via \(h\)-, \(p\)- or \(r\)-adaptivity. In principle, any of the approaches for error assessment may be combined with any of the procedures for adapting the discretization. However, some combinations are clearly preferable. Here we discuss advantages and limitations of various alternatives. The most adequate strategies are illustrated by means of several applications in solid mechanics.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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