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 …

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 …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …

The standard a priori error analysis of discontinuous Galerkin methods requires additional
regularity on the solution of the elliptic boundary value problem in order to justify the …

We propose and analyse a new finite-element method for convection–diffusion problems
based on the combination of a mixed method for the elliptic and a discontinuous Galerkin …

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for
second-order elliptic partial differential equations, and a priori error estimates were …

We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric
second order linear elliptic operators. The method is formulated on nonconforming meshes …

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