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

Yanli Chen & Yonghai Li

DOI: 10.4208/aamm.2013.m401

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 O(h 3 ) convergence rate in H1 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 = {Yanli Chen and Yonghai Li}, 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 O(h 3 ) convergence rate in H1 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 - Yanli Chen & Yonghai Li JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 454 EP - 471 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2013.m401 UR - https://global-sci.org/intro/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 O(h 3 ) convergence rate in H1 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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