Yanli Chen and
Yonghai Li
10.4208/aamm.2013.m401
Adv. Appl. Math. Mech., 7 (2015), pp. 454-471.
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 O(h
3
) convergence rate in H1 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.
