A finite volume method for Stokes problems on quadrilateral meshes
Publication date: Available online 13 November 2018
Source: Computers & Mathematics with Applications
Author(s): Tie Zhang, Zheng Li
We present a finite volume method for Stokes problems using the isoparametric – element pair on quadrilateral meshes. To offset the lack of the – 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 - and -norms for velocity and in the -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.