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.