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 …

In this article, we address adaptive methods for isogeometric analysis based on local
refinement guided by recovery based a posteriori error estimates. Isogeometric analysis was …

A new residual type flux-free error estimator is presented. It estimates upper and lower
bounds of the error in energy norm. The proposed approach precludes the main drawbacks …

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 background of error estimation and adaptivity in finite element computations - ScienceDirect
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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 …

We present a method for the computation of upper and lower bounds for linear-functional
outputs of the exact solutions to the two dimensional elasticity equations. The method can be …

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 …

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 …

The paper introduces a methodology to compute strict upper and lower bounds for linear-
functional outputs of the exact solutions of the advection-reaction-diffusion equation. The …