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Volume 7, Issue 1
Cell Centered Finite Volume Methods Using Taylor Series Expansion Scheme Without Fictitious Domains

G.-M. Gie & R. Temam

Int. J. Numer. Anal. Mod., 7 (2010), pp. 1-29.

Published online: 2010-07

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  • Abstract

The goal of this article is to study the stability and the convergence of cell-centered finite volumes (FV) in a domain $\Omega= (0,1)\times(0,1)\subset R^2$ with non-uniform rectangular control volumes. The discrete FV derivatives are obtained using the Taylor Series Expansion Scheme (TSES), (see [4] and [10]), which is valid for any quadrilateral mesh. Instead of using compactness arguments, the convergence of the FV method is obtained by comparing the FV method to the associated finite differences (FD) scheme. As an application, using the FV discretizations, convergence results are proved for elliptic equations with Dirichlet boundary condition.

  • Keywords

Finite volume methods, finite difference methods, Taylor series expansion scheme (TSES), convergence and stability, elliptic equations.

  • AMS Subject Headings

65N12, 65N25, 76M12, 76M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-1, author = {Gie , G.-M. and Temam , R.}, title = {Cell Centered Finite Volume Methods Using Taylor Series Expansion Scheme Without Fictitious Domains}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {1}, pages = {1--29}, abstract = {

The goal of this article is to study the stability and the convergence of cell-centered finite volumes (FV) in a domain $\Omega= (0,1)\times(0,1)\subset R^2$ with non-uniform rectangular control volumes. The discrete FV derivatives are obtained using the Taylor Series Expansion Scheme (TSES), (see [4] and [10]), which is valid for any quadrilateral mesh. Instead of using compactness arguments, the convergence of the FV method is obtained by comparing the FV method to the associated finite differences (FD) scheme. As an application, using the FV discretizations, convergence results are proved for elliptic equations with Dirichlet boundary condition.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/708.html} }
TY - JOUR T1 - Cell Centered Finite Volume Methods Using Taylor Series Expansion Scheme Without Fictitious Domains AU - Gie , G.-M. AU - Temam , R. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 29 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/708.html KW - Finite volume methods, finite difference methods, Taylor series expansion scheme (TSES), convergence and stability, elliptic equations. AB -

The goal of this article is to study the stability and the convergence of cell-centered finite volumes (FV) in a domain $\Omega= (0,1)\times(0,1)\subset R^2$ with non-uniform rectangular control volumes. The discrete FV derivatives are obtained using the Taylor Series Expansion Scheme (TSES), (see [4] and [10]), which is valid for any quadrilateral mesh. Instead of using compactness arguments, the convergence of the FV method is obtained by comparing the FV method to the associated finite differences (FD) scheme. As an application, using the FV discretizations, convergence results are proved for elliptic equations with Dirichlet boundary condition.

Gie , G.-M. and Temam , R.. (2010). Cell Centered Finite Volume Methods Using Taylor Series Expansion Scheme Without Fictitious Domains. International Journal of Numerical Analysis and Modeling. 7 (1). 1-29. doi:
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