TY - JOUR
T1 - Nonconforming Finite Volume Methods for Second Order Elliptic Boundary Value Problems
AU - Yuanyuan Zhang & Zhongying Cheng
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 381
EP - 404
PY - 2017
DA - 2017/06
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10013.html
KW - Nonconforming finite volume method, elliptic boundary value problems.
AB - <p style="text-align: justify;">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.</p>