@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 = {<p style="text-align: justify;">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&nbsp;$\mathcal{O}(h^3)$ 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2013.m401},
url = {http://global-sci.org/intro/article_detail/aamm/12058.html}
}