Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes
Year: 2005
Author: Weizhang Huang
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 1 : pp. 57–74
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-920
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 1 : pp. 57–74
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: mesh adaptation equidistribution error analysis finite element method.