This work provides an overview of a posteriori error assessment techniques for Finite Element
(FE) based numerical models. These tools aim at estimating and controlling the discretization
error in scientific computational models being the basis for the numerical verification of the
FE solutions. The text discusses the capabilities and limitations of classical methods to build
error estimates which can be used to control the quality of numerical simulations and drive
adaptive algorithms with a focus on Computational Mechanics engineering applications.
Fundamentals principles of residual methods smoothing (recovery) methods and constitutive
relation error (duality based) methods are thus addressed along the manuscript. Attention is
paid to recent advances and forthcoming research challenges on related topics. The book
constitutes a useful guide for students researchers or engineers wishing to acquire insights
into state-of-the-art techniques for numerical verification.
