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Error estimates for the three-field formulation with bubble stabilization


Authors: Franco Brezzi and Donatella Marini
Journal: Math. Comp. 70 (2001), 911-934
MSC (2000): Primary 65N55, 65N30, 65N12, 65N15, 35J25
DOI: https://doi.org/10.1090/S0025-5718-00-01250-3
Published electronically: March 24, 2000
MathSciNet review: 1826573
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Abstract | References | Similar Articles | Additional Information

Abstract:

In this paper we prove convergence and error estimates for the so-called 3-field formulation using piecewise linear finite elements stabilized with boundary bubbles. Optimal error bounds are proved in $L^2$ and in the broken $H^1$ norm for the internal variable $u$, and in suitable weighted $L^2$norms for the other variables $\lambda$ and $\psi$.


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Additional Information

Franco Brezzi
Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy; Istituto di Analisi Numerica del CNR, via Ferrata 1, 27100 Pavia, Italy
Email: brezzi@dragon.ian.pv.cnr.it

Donatella Marini
Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy; Istituto di Analisi Numerica del CNR, via Ferrata 1, 27100 Pavia, Italy
Email: marini@dragon.ian.pv.cnr.it

DOI: https://doi.org/10.1090/S0025-5718-00-01250-3
Received by editor(s): February 2, 1999
Received by editor(s) in revised form: August 5, 1999
Published electronically: March 24, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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