Convergence analysis of finite element solution of one dimensional singularly perturbed differential equations on equidistributing meshes
Weizhang Huang 11 Department of Mathematics, the University of Kansas, Lawrence, KS 66045, USA
Received by the editors January 1, 2004 and, in revised form, March 22, 2004.
In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is given for finite element solution of singularly perturbed two-point boundary value problems without turning points. Illustrative numerical results are given for a convection-diffusion problem and a reaction-diffusion problem.
AMS subject classifications: 65M50, 65M60, 65L50, 65L60
Key words: mesh adaptation; equidistribution; error analysis; finite element method