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Graded Meshes for Higher Order FEM

Graded Meshes for Higher Order FEM
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Year:    2015

Author:    Hans-Görg Roos, L. Teofanov, Zorica Uzelac

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 1–16

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1405-m4362

Journal of Computational Mathematics, Vol. 33 (2015), Iss. 1 : pp. 1–16

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Singular perturbation Boundary value problem Layer-adapted meshes Graded meshes Finite element method.

Author Details

Hans-Görg Roos

L. Teofanov

Zorica Uzelac

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