Analysis of some mixed finite element methods related to reduced integration

We prove error estimates for the following two mixed finite element methods related to reduced integration: A method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure, and one method for a plate prob...

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Bibliographic Details
Published in:Mathematics of computation 1982, Vol.38 (158), p.375-400
Main Authors: Claes Johnson, Juhani Pitkäranta
Format: Article
Language:English
Subjects:
Approximation
College mathematics
Estimation methods
Finite element method
Mathematical functions
Mathematical integration
Mathematics
Rectangles
Rotation
Zero
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Summary:We prove error estimates for the following two mixed finite element methods related to reduced integration: A method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure, and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress. The main idea of the proof in the case of Stokes' problem is to combine a weak Babuška-Brezzi type stability estimate for the pressure with a superapproximability property for the velocities. A similar technique is used in the case of the plate problem.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1982-0645657-2