Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

Year:    2015

Author:    Yanli Chen, Yonghai Li

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 454–471

Abstract

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2013.m401

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 454–471

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:   

Author Details

Yanli Chen

Yonghai Li

  1. High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions

    Zhou, Yanhui | Wu, Jiming

    Computers & Mathematics with Applications, Vol. 92 (2021), Iss. P.1

    https://doi.org/10.1016/j.camwa.2021.03.022 [Citations: 8]
  2. A family of quadratic finite volume element schemes for anisotropic diffusion problems on triangular meshes

    Zhou, Yanhui | Wu, Jiming

    Journal of Computational and Applied Mathematics, Vol. 402 (2022), Iss. P.113794

    https://doi.org/10.1016/j.cam.2021.113794 [Citations: 3]
  3. A unified analysis of a class of quadratic finite volume element schemes on triangular meshes

    Zhou, Yanhui | Wu, Jiming

    Advances in Computational Mathematics, Vol. 46 (2020), Iss. 5

    https://doi.org/10.1007/s10444-020-09809-8 [Citations: 15]