CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Error Analysis of the Finite Volume Element Method for 
         Elliptic and Parabolic Partial Differential Equations
 

SPEAKER: Rick V. Trujillo, Department of Mathematics, UCD

DATE:    Tuesday, May 14, 1996  (PLEASE NOTE UNUSUAL DAY AND TIME)

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 - 3:30 pm 



ABSTRACT

An a priori error analysis of the finite volume element method, 
a locally conservative, Petrov-Galerkin, finite element method  
for the numerical solution of elliptic and parabolic partial differential 
equations arising in fluid dynamics applications, is presented. 
Existing error estimates apply to discretizations of steady diffusion 
equations by linear finite elements in two spatial dimensions. 
These results are extended to steady advection-reaction-diffusion 
equations and are generalized to polynomial finite elements of 
arbitrary order in three spatial dimensions and to the full range 
of admissible regularities for the exact solution.
Optimal-order error estimates for h, p, and h-p versions of the method 
with uniform refinement are derived in a discrete H^1 norm, 
under minimal regularity assumptions for the exact solution, 
the finite element triangulation, and the finite volume construction.
With additional symmetry assumptions for the finite volumes, 
multi-dimensional H^1 superconvergence results are obtained for 
linear finite elements. Using an elliptic projection argument, 
we outline the analysis of continuous-time and backward Euler and 
Crank-Nicolson discrete-time methods for general parabolic equations.