This article is a review of basic concepts and tools devoted to a posteriori error estimation for
problems solved with the finite element method. For the sake of simplicity and clarity, we …

This work presents an analysis methodology based on the use of the Finite Element Method
(FEM) nowadays considered one of the main numerical tools for solving Boundary Value …

We present a simple error estimation and mesh adaptation approach for 3D linear elastic
crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global …

A new stress recovery procedure that provides accurate estimations of the discretization
error for linear elastic fracture mechanic problems analyzed with the extended finite element …

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the
local error in quantities of interest (QoI), which are often more pertinent than local errors in …

This paper introduces a new recovery‐type error estimator ensuring local equilibrium and
yielding a guaranteed upper bound of the error. The upper bound property requires the …

This paper introduces a recovery-type error estimator yielding upper bounds of the error in
energy norm for linear elastic fracture mechanics problems solved using the extended finite …

This article presents a computationally efficient and straightforward to implement a posteriori
error estimator for second‐order G/XFEM and FEM approximations. The formulation is …

Structural optimization is part of the mechanical engineering field and, in most cases, tries to
minimize the overall weight of a given design domain, subjected to functionality constraints …

The extended finite element method (XFEM) is now one of many successful numerical
methods to solve fracture mechanics problems. The particular advantage of the XFEM …