Anisotropic mesh refinement in stabilized Galerkin methods (Q1923303)

This paper is concerned with the finite element solution of the following elliptic boundary value problem in a bounded polyhedral domain \( \Omega \subseteq\mathbb{R}^d, d=2,3\), with Lipschitz boundary \( \partial \Omega \): \[ -\epsilon \Delta u+b\cdot\nabla u+c u=f\quad \text{in} \Omega,\quad u=0 \quad \text{on} \partial\Omega, \] \(\epsilon \in (0,1]\) is a parameter. The aim is to extend the numerical analysis of the Galerkin/least squares methods to meshes which are anisotropically refined at least in the boundary layers to derive error estimates in the energy norm uniformly with respect to \( \epsilon \in (0,1] \). At the end an application to problems of channel type is presented.