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Error estimates for the three-field formulation with bubble stabilization
Authors:Franco Brezzi  Donatella Marini
Institution:Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy; Istituto di Analisi Numerica del CNR, via Ferrata 1, 27100 Pavia, Italy ; Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy; Istituto di Analisi Numerica del CNR, via Ferrata 1, 27100 Pavia, Italy
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 $\psi$.

Keywords:
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