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 …

Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

Bibliography Page 1 Bibliography [1] Y. Achdou, C. Bernardi, and F. Coquel, A priori and a
posteriori analysis of finite volume dis- cretizations of Darcy’s equations, Numer. Math. 96 (2003) …

This paper introduces a quasi-interpolation operator for scalar-and vector-valued finite
element spaces constructed on affine, shape-regular meshes with some continuity across …

We establish residual a posteriori error estimates for lowest-order Raviart–Thomas mixed
finite element discretizations of convection-diffusion-reaction equations on simplicial …

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 …

The importance of accuracy verification methods was understood at the very beginning of
the development of numerical analysis. Recent decades have seen a rapid growth of results …

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) …