Computational Methods in Applied Mathematics
Lagrange equations, Finite element method, Differential equations
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 ux 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.
Gopalakrishnan, J. (2003). A Schwarz Preconditioner for a Hybridized Mixed Method. Computational Methods in Applied Mathematics, Vol. 3, No. 1, pp. 116-134.