Adaptive stabilized mixed finite volume methods for the incompressible flow

作者：Li, Jian^*; Chen, Zhangxin; Zhang, Tong

来源：Numerical Methods for Partial Differential Equations, 2015, 31(5): 1424-1443.

DOI：10.1002/num.21950

• adaptive finite volume method
• error reduction
• stabilized methods
• Stokes equations
• upper and lower bounds

In this article, we study adaptive stabilized mixed finite volume methods for the incompressible flows approximated using the lower order elements. A residual type of a posteriori error estimator is designed and studied with the derivation of upper and lower bounds between the exact solution and the finite volume solution. A discrete local lower bound between two successive finite volume solutions is also obtained. Also, convergence of the adaptive stabilized mixed finite volume methods is established. The presented methods have three prominent features. First, it is of practical convenience in real applications with the same partitions for velocity and pressure. Second, less computational time is required by easily applying both the lower order elements and the local grid refinement necessary for the elements of interest. Third, compared with the standard finite element method, its analysis of H-1-norm and L-2-norm for the velocity and pressure are usually derived without any high order regularity conditions on the exact solution.

• 出版日期2015-9
• 单位西安交通大学; 河南理工大学; 宝鸡文理学院; 西北工业大学