A singularly perturbed problem with two parameters on a Bakhvalov-type mesh

Abstract

© 2015 Elsevier B.V. All rights reserved. A singularly perturbed problem with two small parameters is considered. On a Bakhvalov-type mesh we prove uniform convergence of a Galerkin finite element method with piecewise linear functions. Arguments in the error analysis include interpolation error bounds for a Clément quasi-interpolant as well as discretization error estimates in an energy norm. Numerical experiments support theoretical findings.