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Indexed by:期刊论文

Date of Publication:2016-03-01

Journal:APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B

Included Journals:SCIE

Volume:31

Issue:1

Page Number:21-36

ISSN No.:1005-1031

Key Words:Stokes equations; nonconforming finite element; macroelement; stability

Abstract:In this paper, the quadratic nonconforming brick element (MSLK element) introduced in [10] is used for the 3D Stokes equations. The instability for the mixed element pair MSLK-P (1) is analyzed, where the vector-valued MSLK element approximates the velocity and the piecewise P (1) element approximates the pressure. As a cure, we adopt the piecewise P (1) macroelement to discretize the pressure instead of the standard piecewise P (1) element on cuboid meshes. This new pair is stable and the optimal error estimate is achieved. Numerical examples verify our theoretical analysis.