A Schwarz Preconditioner for a Hybridized Mixed Method

By Jay Gopalakrishnan. 2003

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Abstract In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the flux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest-order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to precondition even the higher-order cases of these methods.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/92c77f5fe22cd1fb9b3782c8bd33d7ed1b426a0a

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Multigrid for an HDG method (2013, methodology): “See (Gopalakrishnan, 2003, Proof of Theorem 2.3).”