This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

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

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 …

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

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 derive a posteriori error estimates for a class of second-order monotone quasi-linear
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …

We consider the a posteriori error analysis of approximations of parabolic problems based
on arbitrarily high-order conforming Galerkin spatial discretizations and arbitrarily high-order …

Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is
developed. It is based on H^ 1_0 (Ω)^ d-conforming velocity reconstruction and H (div, Ω) …

This work proposes a novel finite volume paradigm, ie, the face‐centred finite volume
(FCFV) method. Contrary to the popular vertex and cell‐centred finite volume methods, the …