This work reviews goal-oriented a posteriori error control, adaptivity and solver control for
finite element approximations to boundary and initial-boundary value problems for stationary …

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 …

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

A finite element-based image segmentation strategy enhanced by an anisotropic mesh
adaptation procedure is presented. The methodology relies on a split Bregman algorithm for …

We derive a unified framework for goal-oriented a posteriori estimation covering in particular
higher-order conforming, nonconforming, and discontinuous Galerkin finite element …

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized
via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point …

We present a unified framework for goal-oriented estimates for elliptic and parabolic
problems that combines the dual-weighted residual method with equilibrated flux and …

The parametric analysis of electric grids requires carrying out a large number of power flow
computations. The different parameters describe loading conditions and grid properties. In …

In this paper, we study the a posteriori error estimate corresponding to the Brinkman–Darcy–
Forchheimer problem. We introduce the variational formulation discretized by using the finite …

The quality of a local physical quantity obtained by the numerical method, such as the finite
element method (FEM), attracts more and more attention in computational …