Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 3 : pp. 381–404
Abstract
This paper is devoted to the analysis of nonconforming finite volume methods (FVMs), whose trial spaces are chosen as the nonconforming finite element (FE) spaces, for solving the second order elliptic boundary value problems. We formulate the nonconforming FVMs as special types of Petrov-Galerkin methods and develop a general convergence theorem, which serves as a guide for the analysis of the nonconforming FVMs. As special examples, we shall present the triangulation based Crouzeix-Raviart (C-R) FVM as well as the rectangle mesh based hybrid Wilson FVM. Their optimal error estimates in the mesh dependent $H^1$-norm will be obtained under the condition that the primary mesh is regular. For the hybrid Wilson FVM, we prove that it enjoys the same optimal error order in the $L^2$-norm as that of the Wilson FEM. Numerical experiments are also presented to confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10013
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 3 : pp. 381–404
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Nonconforming finite volume method elliptic boundary value problems.