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A simple error estimator and adaptive procedure for practical engineering analysis. (English) Zbl 0602.73063
A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes. The estimator allows the global energy norm error to be well estimated and also gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials. When combined with an automatic mesh generator a very efficient guidance process to analysis is available. Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.

74S05Finite element methods in solid mechanics
65N15Error bounds (BVP of PDE)
65M15Error bounds (IVP of PDE)