The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

This monograph is centered on mathematical modeling, innovative numerical algorithms
and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art …

We present equilibrated flux a posteriori error estimates in a unified setting for conforming,
nonconforming, discontinuous Galerkin, and mixed finite element discretizations of the two …

Water and air behave in a similar way and their flow can be described in a very accurate
way by the Navier–Stokes equations. Others fluids behave differently: they cannot be …

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 …

We present and analyze an enriched Galerkin finite element method (EG) to solve elliptic
and parabolic equations with jump coefficients. EG is formulated by enriching the …

For linear problems, domain decomposition methods can be used directly as iterative
solvers but also as preconditioners for Krylov methods. In practice, Krylov acceleration is …

Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …

In this paper, an adaptive refinement technique using the scaled boundary finite element
method (SBFEM) is proposed. The salient feature of this technique is that it is not required to …

In this work, we derive two-sided a posteriori error estimates for the dual-weighted residual
(DWR) method. We consider both single and multiple goal functionals. Using a saturation …