A-POSTERIORI ERROR ESTIMATION IN LEAST-SQUARES STABILIZED FINITE-ELEMENT SCHEMES

We introduce a new approach to a posteriori error estimation in finite element Galerkin schemes with least-squares stabilization. Typical ex amples are the stabilization of equal-order approximation in mixed fin ite element schemes and the streamline-diffusion method for convection -dominated problems. The underlying framework is the general optimal-c ontrol approach recently proposed for error control in finite element models. In this method the approximate solutions of certain dual probl ems are used as weighting factors in residual-based a posteriori bound s for arbitrary functionals of the error. On this basis almost optimal ly economical meshes as well as reliable and efficient error bounds ca n be developed in a feed-back process on successively adapted meshes. The new feature in this method when applied for least-squares finite e lement methods is the use of mesh-dependent duality arguments to guara ntee optimal-order estimation of the stabilization terms. (C) 1998 Els evier Science S.A. All rights reserved.