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Volume 16, Issue 3
FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer

Simon Becher

Int. J. Numer. Anal. Mod., 16 (2019), pp. 499-518.

Published online: 2018-11

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  • 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.

  • Keywords

Singular perturbation, turning point, interior layer, layer-adapted meshes, higher order finite elements.

  • AMS Subject Headings

65L10, 65L50, 65L60, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Simon.Becher@tu-dresden.de (Simon Becher)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-16-499, author = {Becher , Simon}, title = {FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12879.html} }
TY - JOUR T1 - FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer AU - Becher , Simon JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 499 EP - 518 PY - 2018 DA - 2018/11 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12879.html KW - Singular perturbation, turning point, interior layer, layer-adapted meshes, higher order finite elements. AB -

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.

Becher , Simon. (2018). FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer. International Journal of Numerical Analysis and Modeling. 16 (3). 499-518. doi:
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