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

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

We propose and analyze a numerical scheme for nonlinear degenerate parabolic
convection–diffusion–reaction equations in two or three space dimensions. We discretize …

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

We prove several discrete Gagliardo–Nirenberg–Sobolev and Poincaré–Sobolev
inequalities for some approximations with arbitrary boundary values on finite volume …

We study extensions of piecewise polynomial data prescribed on faces and possibly in
elements of a patch of simplices sharing a vertex. In the $ H^ 1$ setting, we look for functions …