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 …

A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the
incompressible Navier–Stokes equations is presented. The key ingredient is an accurate …

SUMMARY A p‐adaptive hybridizable discontinuous Galerkin method for the solution of
wave problems is presented in a challenging engineering problem. Moreover, its …

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 present a method for the automatic adaption of the support size of meshfree basis
functions in the context of the numerical approximation of boundary value problems …

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable
discontinuous Galerkin (HDG) approach is presented for the first time. The proposed …

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 define an a posteriori verification procedure that enables to control and certify PGD-
based model reduction techniques applied to parametrized linear elliptic or parabolic …

Abstract Numerical Model Reduction (NMR) is exploited for solving the finite element
problem on a Representative Volume Element (RVE) that arises from the computational …