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Volume 3, Issue 4
A Mesh Adaptation Method for 1D-Boundary Layer Problems

ANDRÉ FORTIN, JOSÉ M. URQUIZA, AND RICHARD BOIS

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 408-428

Published online: 2012-03

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  • Abstract
We present a one-dimensional version of a general mesh adaptation technique developed in [1, 2] which is valid for two and three-dimensional problems. The simplicity of the one-dimensional case allows to detail all the necessary steps with very simple computations. We show how the error can be estimated on a piecewise finite element of degree k and how this information can be used to modify the grid using local mesh operations: element division, node elimination and node displacement. Finally, we apply the whole strategy to many challenging singularly perturbed boundary value problems where the one-dimensional setting allows to push the adaptation method to its limits.
  • Keywords

hierarchical error estimation mesh adaptation singular perturbation boundary layer problems

  • AMS Subject Headings

65G20 65N12 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-408, author = {ANDRÉ FORTIN, JOSÉ M. URQUIZA, AND RICHARD BOIS}, title = {A Mesh Adaptation Method for 1D-Boundary Layer Problems}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {4}, pages = {408--428}, abstract = {We present a one-dimensional version of a general mesh adaptation technique developed in [1, 2] which is valid for two and three-dimensional problems. The simplicity of the one-dimensional case allows to detail all the necessary steps with very simple computations. We show how the error can be estimated on a piecewise finite element of degree k and how this information can be used to modify the grid using local mesh operations: element division, node elimination and node displacement. Finally, we apply the whole strategy to many challenging singularly perturbed boundary value problems where the one-dimensional setting allows to push the adaptation method to its limits.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/292.html} }
TY - JOUR T1 - A Mesh Adaptation Method for 1D-Boundary Layer Problems AU - ANDRÉ FORTIN, JOSÉ M. URQUIZA, AND RICHARD BOIS JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 408 EP - 428 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/292.html KW - hierarchical error estimation KW - mesh adaptation KW - singular perturbation KW - boundary layer problems AB - We present a one-dimensional version of a general mesh adaptation technique developed in [1, 2] which is valid for two and three-dimensional problems. The simplicity of the one-dimensional case allows to detail all the necessary steps with very simple computations. We show how the error can be estimated on a piecewise finite element of degree k and how this information can be used to modify the grid using local mesh operations: element division, node elimination and node displacement. Finally, we apply the whole strategy to many challenging singularly perturbed boundary value problems where the one-dimensional setting allows to push the adaptation method to its limits.
ANDRÉ FORTIN, JOSÉ M. URQUIZA, AND RICHARD BOIS. (2012). A Mesh Adaptation Method for 1D-Boundary Layer Problems. International Journal of Numerical Analysis Modeling Series B. 3 (4). 408-428. doi:
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