13 - Errors, recovery processes and error estimates

Abstract

This chapter is designed to discuss errors, recovery processes, and error estimates. The objectives of this chapter are concerned with the question of accuracy and a possible improvement on it by a posteriori treatments of the finite element data. Such processes are referred to as recovery. This chapter presents the discretization error of the finite element approximation and a posteriori estimates of such error. In particular, it describes two distinct types of aposteriori error estimators: recovery-based error estimators and residual-based error estimators. This chapter discusses the importance of highly accurate recovery methods in the computation of the recovery-based error estimators is discussed. It also demonstrates how various recovery methods can be used in the construction of residual-based error estimators. Additionally, it demonstrates that estimators based on Superconvergent Patch Recovery (SPR) are superior to those based on residual computation.