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Volume 5, Issue 4
A Pre-Processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

P. F. Antonietti & P. Houston

Int. J. Numer. Anal. Mod., 5 (2008), pp. 704-728.

Published online: 2008-05

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  • Abstract

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

  • Keywords

discontinuous Galerkin methods, advection-diffusion problems, adaptivity.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-704, author = {P. F. Antonietti and P. Houston}, title = {A Pre-Processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {4}, pages = {704--728}, abstract = {

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/834.html} }
TY - JOUR T1 - A Pre-Processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems AU - P. F. Antonietti & P. Houston JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 704 EP - 728 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/834.html KW - discontinuous Galerkin methods, advection-diffusion problems, adaptivity. AB -

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

P. F. Antonietti and P. Houston. (2008). A Pre-Processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems. International Journal of Numerical Analysis and Modeling. 5 (4). 704-728. doi:
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