Weighted a Posteriori Error Control in Fe Methods

The conventional strategy for controlling the error in nite element (FE) methods is based on a posteriori estimates for the error in the global energy or L 2 norm involving local residuals of the computed solution (error indicators). Such estimates are derived via duality arguments where the approximation properties of the nite element space enter through local interpolation constants while the stability of the (linearized) dual problem is usually expressed in terms of a global stability constant. The mesh reenement process is then oriented at the equilibration of the local error indicators. However, meshes generated in this way via controlling the error in a global norm may not be appropriate for local error quantities like point values or contour integrals. In this note a reened approach to residual{based error estimation is proposed where certain quantities involving the dual solution are used as weight-factors in order to capture information about the local error propagation. In this way "optimal" meshes may be generated for various types of error measures. This is illustrated at simple model cases. One practical application of this approach is, for example, the computation of drag and lift coeecients of blunt bodies in viscous ows governed by the Navier-Stokes equations. 1