Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, an optimal bicubic finite volume method is established andanalyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwisestiffness matrix analysis technique, we proceed the stability analysis. It is provedthat 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, numericalexamples are provided to confirm the theoretical analysis of bicubic finite volumemethod.