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 - <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>