Title: Averaging Based Estimators for Elliptic Equations

Speaker: Varis Carey, Cornell University
 
Date/Time: Monday, March 28, 2005, 9:00-10:00 am

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: Averaging operators provide inexpensive and robust error control for finite element discretization of elliptic PDEs.  We present a framework, first introduced by Schatz and Wahlbin, that modifies existing popular recovery operators (such as the Zienkiewicz-Zhu Estimator) to produce estimators that are locally bounded in maximum-norm, and can produce asymptotically exact estimators on unstructured meshes.  We illustrate the excellent performance of these operators in the preasymptotic range with a variety of numerical examples.  Certain features of the averaging operators that make them very convenient for parallel computation are also detailed. In addition, we give new numerical results illustrating the effective use of these operators on problems with "pollution", and develop a similar framework of local error control for function values, employing some recent local negative-norm a priori estimates of Schatz.