Analysis of some mixed finite element methods related to reduced integration

Authors:
Claes Johnson and Juhani Pitkäranta

Journal:
Math. Comp. **38** (1982), 375-400

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645657-2

MathSciNet review:
645657

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Abstract: 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.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0645657-2

Article copyright:
© Copyright 1982
American Mathematical Society