Performance of several stabilized finite element methods for the Stokes equations based on the lowest equal-order pairs

Authors:
Jian Li;Yinnian He;Zhangxin Chen
Affiliations:
Baoji Univ. of Arts and Sci., Dept. of Math., 721007, Baoji, PRC Xi’an Jiaotong Univ., Fac. of Sci., 710049, Xi’an, PRC and Univ. of Calgary, Dept. of Chem. and Petroleum Eng., Schul ...;Xi’an Jiaotong University, Faculty of Science, 710049, Xi’an, People’s Republic of China;Xi’an Jiaotong Univ., Fac. of Sci., 710049, Xi’an, PRChina and University of Calgary, Dept. of Chemical and Petroleum Engineering, Schulich School of Engineering, 2500 University Dri ...
Venue:
Computing
Year:
2009

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Abstract

In this paper the performance of various stabilized mixed finite element methods based on the lowest equal-order polynomial pairs (i.e., P 1 − P 1 or Q 1 − Q 1) are numerically investigated for the stationary Stokes equations: penalty, regular, multiscale enrichment, and local Gauss integration methods. Comparisons between them will be carried out in terms of the critical factors: stabilization parameters, convergence rates, consistence, and mesh effects. It is numerically drawn that the local Gauss integration method is a favorite method among these methods.