A second-order hybrid finite volume method for solving the Stokes equation

作者：Chen, Zhongying; Xu, Yuesheng^*; Zhang, Jiehua

来源：Applied Numerical Mathematics, 2017, 119: 213-224.

DOI：10.1016/j.apnum.2017.04.002

• Finite volume method
• Stokes equation
• Inf-sup conditions

This paper presents a second-order hybrid finite volume method for solving the Stokes equation on a two dimensional domain. The trial function space of the method for velocity is chosen to be a quadratic conforming finite element space with a hierarchical decomposition technique on triangular meshes, and its corresponding test function space consists of piecewise constant functions and piecewise quadratic polynomial functions based on a dual partition of the domain. The trial function space and test function space of the method for pressure are chosen to be a linear finite element space. We derive the inf-sup conditions of the discrete systems of the method on triangular meshes by using a relationship between the finite volume method and the finite element method. The well-posedness of the proposed finite volume method is obtained by using the Babuska-Lax-Milgram theorem. The error estimates of the optimal order are obtained in the H-1-norm for velocity and in the L-2-norm for pressure. Numerical experiments are presented to illustrate the theoretical results.

• 出版日期2017-9
• 单位凯里学院; 中山大学