Year: 2019
Author: Simon Becher
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 499–518
Abstract
We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted graded meshes proposed by Liseikin. We prove $ε$-uniform error estimates in the energy norm. Furthermore, for linear elements we are able to prove optimal order $ε$-uniform convergence in the $L$2-norm on these graded meshes.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12879
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 3 : pp. 499–518
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Singular perturbation turning point interior layer layer-adapted meshes higher order finite elements.