Volume 7, Issue 4
Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

Adv. Appl. Math. Mech., 7 (2015), pp. 454-471.

Published online: 2018-05

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• Abstract

In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal $\mathcal{O}(h^3)$ convergence rate in $H^1$ norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

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@Article{AAMM-7-454, author = {Chen , Yanli and Li , Yonghai}, title = {Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {4}, pages = {454--471}, abstract = {

In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal $\mathcal{O}(h^3)$ convergence rate in $H^1$ norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m401}, url = {http://global-sci.org/intro/article_detail/aamm/12058.html} }
TY - JOUR T1 - Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes AU - Chen , Yanli AU - Li , Yonghai JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 454 EP - 471 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m401 UR - https://global-sci.org/intro/article_detail/aamm/12058.html KW - AB -

In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal $\mathcal{O}(h^3)$ convergence rate in $H^1$ norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

Yanli Chen & Yonghai Li. (1970). Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes. Advances in Applied Mathematics and Mechanics. 7 (4). 454-471. doi:10.4208/aamm.2013.m401
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