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.
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