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Article
A Schwarz Preconditioner for a Hybridized Mixed Method
Computational Methods in Applied Mathematics
  • Jay Gopalakrishnan, Portland State University
Document Type
Article
Publication Date
1-1-2003
Subjects
  • Lagrange equations,
  • Finite element method,
  • Differential equations
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 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.
Description

This is the publisher's final PDF. The final publication is available at www.degruyter.com

DOI
10.2478/cmam-2003-0009
Persistent Identifier
http://archives.pdx.edu/ds/psu/10926
Citation Information
Gopalakrishnan, J. (2003). A Schwarz Preconditioner for a Hybridized Mixed Method. Computational Methods in Applied Mathematics, Vol. 3, No. 1, pp. 116-134.