Varis Carey
Department of Mathematics
Colorado State University
Fort Collins, Colorado, USA
Adaptive methods for solving partial differential equations are often controlled by a posteriori error estimators. These methods are often complicated by non-local sources of error, often referred to as "pollution". We introduce a class of averaging operators, including generalizations of the popular Zienkiewicz-Zhu "Patch Recovery" opeartor, that provide accurate error estimates in non-polluted problems, and accurate local error indicators for polluted problems. The main technical results are for elliptic problems but we will discuss extensions to time-dependent problems and more general differential operators.