Error estimation and control are critical ingredients for improving the reliability of
computational simulations. Adjoint-based techniques can be used to both estimate the error …

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite
element solution of an elliptic linear model problem. We give the basic ideas to establish …

Offering the only existing finite element (FE) codes for Maxwell equations that support hp
refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS …

We give an overview of recent developments concerning the use of adjoint methods in two
areas: the a posteriori error analysis of finite element methods for the numerical solution of …

A method to estimate and control pointwise errors in finite element approximations of elliptic
problems is presented as an application of the more general theory of goal-oriented error …

In this paper a recently developed approach for the design of adaptive discontinuous
Galerkin finite element methods is applied to physically relevant problems arising in inviscid …

Motivated by applications in computational fluid dynamics, a method is presented for
obtaining estimates of integral functionals, such as lift or drag, that have twice the order of …

Most modeling approaches lie in either of the two categories: physics‐based or data‐driven.
Recently, a third approach which is a combination of these deterministic and statistical …

We review and extend the theory and methodology of a posteriori error estimation and
adaptivity for modeling error for certain classes of problems in linear and nonlinear …

Mechanical engineering, an engineering discipline forged and shaped by the needs of the
industrial revolution, is once again asked to do its substantial share in the call for industrial …