Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

A new approach of constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed The linear system arising from the mixed methods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which corresponds to a linear system generated by standard nonconforming nite element methods Algebraic multilevel preconditioners are then constructed for this system based on a triangulation of parallelepipeds into tetrahedral substructures Explicit estimates of condition numbers and simple computational schemes are es tablished for the constructed preconditioners Finally numerical results for the mixed nite element methods are presented to illustrate the present theory