Domain Decomposition Methods in Science and Engineering XVIII

Volume 70 of the series Lecture Notes in Computational Science and Engineering pp 99-109


Auxiliary Space Preconditioners for Mixed Finite Element Methods

  • Ray S. TuminaroAffiliated withMS 9214, Sandia National Laboratories Email author 
  • , Jinchao XuAffiliated withDepartment of Mathematics, Pennsylvania State University
  • , Yunrong ZhuAffiliated withDepartment of Mathematics, University of California, San Diego

* Final gross prices may vary according to local VAT.

Get Access


This paper is devoted to study of an auxiliary spaces preconditioner for H(div) systems and its application in the mixed formulation of second order elliptic equations. Extensive numerical results show the efficiency and robustness of the algorithms, even in the presence of large coefficient variations. For the mixed formulation of elliptic equations, we use the augmented Lagrange technique to convert the solution of the saddle point problem into the solution of a nearly singular H(div) system. Numerical experiments also justify the robustness and efficiency of this scheme.