Gradient weighted residuals for error indicators in FEM and BEM. (English) Zbl 1007.65085
Summary: A simple yet general approach is presented for checking the adequacy of approximate solutions obtained with finite element (FE) and boundary element (BE) weighted residual methods. In this method, which is called the gradient weighted residual technique, the computed residuals in the elements are weighted by appropriate gradients and thereby an indicator of the quality of solution is calculated. Such computations are carried out aposteriori and if need be a reanalysis is then carried out on a new mesh generated on the basis of the quality of the solution determined over the domain.
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
error bounds; finite elements; boundary elements; weighted residuals; error indicators; \(h\)-refinement; a-posteriori estimationReferences:
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