TITLE

GRADED MESHES FOR HIGHER ORDER FEM

AUTHOR(S)
Roos, Hans-Görg; Teofanov, Ljiljana; Uzelac, Zorica
PUB. DATE
January 2015
SOURCE
Journal of Computational Mathematics;2015, Vol. 33 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.
ACCESSION #
100043721

 

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