3 years ago

# A finite volume method for Stokes problems on quadrilateral meshes

Tie Zhang, Zheng Li

Publication date: Available online 13 November 2018

Source: Computers & Mathematics with Applications

Author(s): Tie Zhang, Zheng Li

##### Abstract

We present a finite volume method for Stokes problems using the isoparametric $Q1$$Q0$ element pair on quadrilateral meshes. To offset the lack of the $inf$$sup$ condition, a jump term of discrete pressure (stabilizing term) is added to the continuity approximation equation. Thus, we establish a stabilized finite volume scheme on quadrilateral meshes. Then, based on some superclose estimates, we derive the optimal error estimates in the $H1$- and $L2$-norms for velocity and in the $L2$-norm for pressure, respectively. Numerical examples are provided to illustrate our theoretical analysis. We emphasize that our work is the first time to propose and analyze a finite volume method for Stoke problems using isoparametric elements on quadrilateral meshes.

DOI: S0898122118306412

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