This survey paper contains a surprisingly large amount of material on singularly perturbed
partial differential equations and indeed can serve as an introduction to some of the ideas …

The discontinuous Galerkin finite element method (DGFEM) for the time discretization of
parabolic problems is analyzed in the context of the hp-version of the Galerkin method. Error …

Many partial differential equations arising in practice are parameter-dependent problems
that are of singularly perturbed type. Prominent examples include plate and shell models for …

This paper extends the multi-level hp-approach—previously introduced for the isotropic
refinement of quadrilateral and hexahedral elements—to the anisotropic refinement of …

A singularly perturbed reaction-diffusion equation in two dimensions is considered. We
assume analyticity of the input data, ie, the boundary of the domain is an analytic curve and …

We investigate the application of the discontinuous Petrov–Galerkin (DPG) finite element
framework to stationary convection–diffusion problems. In particular, we demonstrate how …

Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete
inf–sup condition is proved with a constant independent of the meshwidth and the aspect …

The presented article is based on the detection and resolution algorithms that are assigned
to the adaptive finite element methods for solid mechanics problems, in which the boundary …

We consider the numerical approximation of singularly perturbed problems, and in particular
reaction–diffusion problems, by the h version of the finite element method. We present …

We present the analysis of an h version Finite Element Method for the approximation of the
solution to singularly perturbed reaction–diffusion problems posed in smooth domains Ω⊂ …