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Validation of recipes for the recovery of stresses and derivatives by a computer-based approach. (English) Zbl 0811.65092

The methodology for checking the local quantity of recipes for the recovery of stresses or derivatives from finite element solutions of linear elliptic problems is presented. The suggested methodology accounts precisely for the factors which affect the local quantity of the recovered quantities, namely, the geometry of the grid, the polynomial degree and the type of the elements, the coefficients of the differential equation and the class of solutions of interest.
The authors give some examples of how the methodology can be used to obtain precise conclusions about the quality of a class of recipes, based on least squares patch-recovery, in the interior of complex grids, like the ones employed in engineering computations. By using this approach, the authors are able to discover recipes which are much more robust than the ones which are currently in use in the various finite element algorithms.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
35J25 Boundary value problems for second-order elliptic equations
74B10 Linear elasticity with initial stresses
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