Error estimates for the three-field formulation with bubble stabilization

Brezzi, Franco; Marini, Donatella

doi:10.1090/S0025-5718-00-01250-3

Error estimates for the three-field formulation with bubble stabilization
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by Franco Brezzi and Donatella Marini PDF

Math. Comp. 70 (2001), 911-934 Request permission

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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