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This article is a review on basic concepts and tools devoted to a posteriorierror estimation for problems solved with the Finite Element Method. For thesake of simplicity and clarity, we mostly focus on linear elliptic diffusionproblems, approximated by a conforming numerical discretization. The reviewmainly aims at presenting in a unified manner a large set of powerfulverification methods, around the concept of equilibrium. Methods based on thatconcept provide error bounds that are fully computable and mathematicallycertified. We discuss recovery methods, residual methods, and duality-basedmethods for the estimation of the whole solution error (i.e. the error inenergy norm), as well as goal-oriented error estimation (to assess the error onspecific quantities of interest). We briefly survey the possible extensions tonon-conforming numerical methods, as well as more complex (e.g. nonlinear ortime-dependent) problems. We also provide some illustrating numerical exampleson a linear elasticity problem in 3D.

A pedagogical review on a posteriori error estimation in Finite Element computations