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Volume 14, Issue 3
Mixed Finite Volume Method for Elliptic Problems on Non-Matching Multi-Block Triangular Grids

Yanni Gao, Junliang Lv & Lanhui Zhang

Int. J. Numer. Anal. Mod., 14 (2017), pp. 456-476.

Published online: 2017-06

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  • Abstract

This article presents a mixed finite volume method for solving second-order elliptic equations with Neumann boundary conditions. The computational domains can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domains independently, and employ the standard mixed finite volume method within each sub-domain. On the interfaces between different sun-domains, the grids are non-matching. The Robin type boundary conditions are imposed on the non-matching interfaces to enhance the continuity of the pressure and flux. Both the solvability and the first order rate of convergence for this numerical scheme are rigorously proved. Numerical experiments are provided to illustrate the error behavior of this scheme and confirm our theoretical results.

  • Keywords

Mixed finite volume method, error estimate, multi-block domain, non-matching grids.

  • AMS Subject Headings

65N08, 65N12, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-456, author = {Yanni Gao, Junliang Lv and Lanhui Zhang}, title = {Mixed Finite Volume Method for Elliptic Problems on Non-Matching Multi-Block Triangular Grids}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {3}, pages = {456--476}, abstract = {

This article presents a mixed finite volume method for solving second-order elliptic equations with Neumann boundary conditions. The computational domains can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domains independently, and employ the standard mixed finite volume method within each sub-domain. On the interfaces between different sun-domains, the grids are non-matching. The Robin type boundary conditions are imposed on the non-matching interfaces to enhance the continuity of the pressure and flux. Both the solvability and the first order rate of convergence for this numerical scheme are rigorously proved. Numerical experiments are provided to illustrate the error behavior of this scheme and confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10017.html} }
TY - JOUR T1 - Mixed Finite Volume Method for Elliptic Problems on Non-Matching Multi-Block Triangular Grids AU - Yanni Gao, Junliang Lv & Lanhui Zhang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 456 EP - 476 PY - 2017 DA - 2017/06 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10017.html KW - Mixed finite volume method, error estimate, multi-block domain, non-matching grids. AB -

This article presents a mixed finite volume method for solving second-order elliptic equations with Neumann boundary conditions. The computational domains can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domains independently, and employ the standard mixed finite volume method within each sub-domain. On the interfaces between different sun-domains, the grids are non-matching. The Robin type boundary conditions are imposed on the non-matching interfaces to enhance the continuity of the pressure and flux. Both the solvability and the first order rate of convergence for this numerical scheme are rigorously proved. Numerical experiments are provided to illustrate the error behavior of this scheme and confirm our theoretical results.

Yanni Gao, Junliang Lv and Lanhui Zhang. (2017). Mixed Finite Volume Method for Elliptic Problems on Non-Matching Multi-Block Triangular Grids. International Journal of Numerical Analysis and Modeling. 14 (3). 456-476. doi:
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