A stabilized finite element method based on two local Gauss integrations for the Stokes equations

Authors:
Jian Li;Yinnian He
Affiliations:
Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China and Department of Mathematics, Baoji University of Arts and Science, Baoji 721007, PR China;Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

This paper considers a stabilized method based on the difference between a consistent and an under-integrated mass matrix of the pressure for the Stokes equations approximated by the lowest equal-order finite element pairs (i.e., the P"1-P"1 and Q"1-Q"1 pairs). This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. Optimal error estimates are obtained by applying the standard Galerkin technique. Finally, the numerical illustrations agree completely with the theoretical expectations.