In this work, we introduce a consistent error estimator for numerical simulations performed
by means of the proper generalized decomposition (PGD) approximation. This estimator …

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 …

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 …

The computational cost of parametric studies currently represents the major limitation to the
application of simulation-based engineering techniques in a daily industrial environment …

Robust global/goal‐oriented error estimation is used nowadays to control the approximate
finite element (FE) solutions obtained from simulation. In the context of computational …

We develop and compare a number of alternative approaches to obtain guaranteed and
fully computable bounds on the error in quantities of interest of arbitrary order finite element …

We consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …

The paper deals with the accuracy of guaranteed error bounds on outputs of interest
computed from approximate methods such as the finite element method. A considerable …

The paper deals with the constitutive relation error (CRE) concept which has been widely
used over the last 40 years for verification and validation of computational mechanics …

In this paper, we investigate a new procedure for constructing admissible stress tensors that
are needed in some methods for robust global/goal-oriented error estimation. This …