Volume 3, Issue 4
Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 499-522.

Published online: 2010-03

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• Abstract

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The $L^2$ norm and $H^1$ semi-norm error estimates are obtained for the first scheme and the second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• Keywords

Three-dimensional parabolic equation, alternating direction method, finite volume element method, error estimate.

65M08, 65M12, 65M15

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@Article{NMTMA-3-499, author = {}, title = {Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {499--522}, abstract = {

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The $L^2$ norm and $H^1$ semi-norm error estimates are obtained for the first scheme and the second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m99027}, url = {http://global-sci.org/intro/article_detail/nmtma/6011.html} }
TY - JOUR T1 - Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 499 EP - 522 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m99027 UR - https://global-sci.org/intro/article_detail/nmtma/6011.html KW - Three-dimensional parabolic equation, alternating direction method, finite volume element method, error estimate. AB -

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The $L^2$ norm and $H^1$ semi-norm error estimates are obtained for the first scheme and the second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Tongke Wang. (2020). Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations. Numerical Mathematics: Theory, Methods and Applications. 3 (4). 499-522. doi:10.4208/nmtma.2010.m99027
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