Adv. Appl. Math. Mech., 7 (2015), pp. 454-471.
Published online: 2018-05
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m401}, url = {http://global-sci.org/intro/article_detail/aamm/12058.html} }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.