BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-84-30
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Mesh-independent spectra in the moving finite element
               equations
        TYPE:: Manuscript
      AUTHOR:: Wathen, Andrew J.
        DATE:: August 1984
       PAGES:: 28
    ABSTRACT:: We derive the Moving Finite Element (MFE) equations for the
               solution of a scalar evolutionary equation in $d$ space
               dimensions ($d \geq\ 1$) and introduce the elementwise
               approach to MFE. This approach yields a decomposition of the
               mesh- and solution-dependent matrix $A$ in the
               (semi-discretised) non-linear system of ordinary differential
               equations $A(y)y = g(y)$ which forms the basis for proofs of
               eigenvalue clustering. With a simple, specific block diagonal
               preconditioner, $D$, it is shown that the eivenvalue spectrum
               of the preconditioned MFE matrix $D^{-1} A$ is [$\frac{1}{2}
               , 1 + \frac{d}{2}$] independently of the mesh configuration,
               the solution and the number of nodes. A more specific result
               is established for the case $d$ = 1. These results guarantee
               extremely rapid solution techniques using, for example,
               conjugate gradient methods. We show how the analysis extends
               to systems of partial differential equations when a separate
               moving mesh is used for each component.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-84-30