Abstract

Bounds for eigenvalues of selfadjoint problems using finite elements H. Behnke & U. Mertins For the computation of bounds to eigenvalues of selfadjoint problems the method of Rayleigh - Ritz and Temple - Lehmann - Goerisch for upper and lower bounds, respectively, have proven to be very powerful. The application of the Rayleigh - Ritz method using finite elements for non convex domains is very well understood. Up to now all known applications of the Temple - Lehmann - Goerisch method are using ''classical'' trial functions on convex or even rectangular domains or finite elements which are restricted to some special cases. We present general Temple - Lehmann - Goerisch methods, which can be applied to finite elements. These methods require the same regularity as the corresponding Rayleigh - Ritz procedures. Results for partial differential equations of second and fourth order are given.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF2 3XF, U.K. Malcom@cs.cf.ac.uk

N.B. All Mathematics appears in TeX/LaTeX source.

Page last updated 14/05/99 webmaster.cs.cf.ca.uk