A FEEDBACK APPROACH TO ERROR CONTROL IN FINITE-ELEMENT METHODS - APPLICATION TO LINEAR ELASTICITY

Recently a refined approach to error control in finite element (FE) di scretisations has been proposed, Becker and Rannacher (1995b), (1996), which uses weighted a posteriori error estimates derived via duality arguments. The conventional strategies for mesh refinement in FE model s of problems from elasticity theory are mostly based on a posteriori error estimates in the energy norm. Such estimates reflect the approxi mation properties of the finite element ansatz by local interpolation constants while the stability properties of the continuous model enter through a global coercivity constant. However, meshes generated on th e basis of such global error estimates are not appropriate in cases wh ere the domain consists of very heterogeneous materials and for the co mputation of local quantities, e.g., point values or contour integrals . This deficiency is cured by using certain local norms of the dual so lution directly as weights multiplying the local residuals of the comp uted solution. In general, these weights have to be evaluated numerica lly in the course of the refinement process, yielding almost optimal m eshes for various kinds of error measures. This feed-back approach is developed here for primal as well as mixed FE discretisations of the f undamental problem in linear elasticity.