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 book introduces the basic ideas to build discontinuous Galerkin methods and, at the
same time, incorporates several recent mathematical developments. The presentation is to a …

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 …

We propose and study a posteriori error estimates for convection–diffusion–reaction
problems with inhomogeneous and anisotropic diffusion approximated by weighted interior …

For the finite volume discretization of a second-order elliptic model problem, we derive a
posteriori error estimates which take into account an inexact solution of the associated linear …

We derive a posteriori error estimates for the discretization of the heat equation in a unified
and fully discrete setting comprising the discontinuous Galerkin, various finite volume, and …

Local mesh adaptivity serves as a practical tool in numerical simulations to accurately
capture features of interest while reducing computational time and memory requirements. In …

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 article discusses nonconforming finite element methods for convex minimization
problems and systematically derives dual mixed formulations. Duality relations lead to …