M 1011

This talk concerns a robust numerical treatment of an elliptic PDE with high contrast coefficients. A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients become large. We introduce a procedure by which the discrete system obtained from a linear finite element discretization of the given continuum problem is converted into an equivalent linear system of the saddle point type. Then a robust preconditioner for the Lancsoz method of minimized iterations for solving the derived saddle point problem is proposed. Numerical examples demonstrate effectiveness and robustness of the proposed class of preconditioners and show the number of iterations independent of the contrast and the discretization size. This is a joint work with Daria Kurzanova and Yuri Kuznetsov (UH).

Prof. Yuliya Gorb

University of Houston