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Volume 7, Issue 1
Space-Time Adaptation for Purely Diffusive Problems in an Anisotropic Framework

S. Micheletti & S. Perotto

Int. J. Numer. Anal. Mod., 7 (2010), pp. 125-155.

Published online: 2010-07

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  • Abstract

The main goal of this work is the proposal of an efficient space-time adaptive procedure for a cGdG approximation of an unsteady diffusion problem. We derive a suitable a posteriori error estimator where the contribution of the spatial and of the temporal discretization is kept distinct. In particular our interest is addressed to phenomena characterized by temporal multiscale as well as strong spatial directionalities. On the one hand we devise a sound criterion to update the time step, able to follow the evolution of the problem under investigation. On the other hand we exploit an anisotropic triangular adapted grid. The reliability and the efficiency of the proposed error estimator are assessed numerically.

  • Keywords

Space-time adaptation, anisotropic meshes, heat equation, space-time finite elements.

  • AMS Subject Headings

35K20, 65M50, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-125, author = {}, title = {Space-Time Adaptation for Purely Diffusive Problems in an Anisotropic Framework}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {1}, pages = {125--155}, abstract = {

The main goal of this work is the proposal of an efficient space-time adaptive procedure for a cGdG approximation of an unsteady diffusion problem. We derive a suitable a posteriori error estimator where the contribution of the spatial and of the temporal discretization is kept distinct. In particular our interest is addressed to phenomena characterized by temporal multiscale as well as strong spatial directionalities. On the one hand we devise a sound criterion to update the time step, able to follow the evolution of the problem under investigation. On the other hand we exploit an anisotropic triangular adapted grid. The reliability and the efficiency of the proposed error estimator are assessed numerically.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/713.html} }
TY - JOUR T1 - Space-Time Adaptation for Purely Diffusive Problems in an Anisotropic Framework JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 125 EP - 155 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/713.html KW - Space-time adaptation, anisotropic meshes, heat equation, space-time finite elements. AB -

The main goal of this work is the proposal of an efficient space-time adaptive procedure for a cGdG approximation of an unsteady diffusion problem. We derive a suitable a posteriori error estimator where the contribution of the spatial and of the temporal discretization is kept distinct. In particular our interest is addressed to phenomena characterized by temporal multiscale as well as strong spatial directionalities. On the one hand we devise a sound criterion to update the time step, able to follow the evolution of the problem under investigation. On the other hand we exploit an anisotropic triangular adapted grid. The reliability and the efficiency of the proposed error estimator are assessed numerically.

S. Micheletti & S. Perotto. (1970). Space-Time Adaptation for Purely Diffusive Problems in an Anisotropic Framework. International Journal of Numerical Analysis and Modeling. 7 (1). 125-155. doi:
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