Release Time:2019-03-13  Hits:

Indexed by: Journal Article

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: 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.