Chapter 15 - Errors, Recovery Processes, and Error Estimates

Abstract

This chapter is concerned with the accuracy of finite element approximation and the recovery methods to improve it. We also consider the discretization error of the finite element approximation and a posteriori estimates of such error. In particular, we describe two distinct type of a posteriori estimators, recovery-based error estimators and residual-based error estimators. The importance of highly accurate recovery methods in the computation of the recovery-based estimators is discussed. Detailed description of how various recovery methods can be used in the construction of both explicit and implicit residual-based error estimators is presented. The accuracy and robustness of error estimators are analyzed and demonstrated numerically. A brief discuss on error bounds and error estimates for the quantities of interest is also given.