CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Control Volume Mixed Finite Element Methods
 

SPEAKER: Jim Jones, ICASE, Hampton, Virginia 

DATE:    Monday, April 8, 1996 (Please note UNUSUAL DAY)

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

TIME:    2:30-3:30 pm (Refreshments at 2:15 pm)



ABSTRACT


The control volume mixed finite element (CVMFE) method
is a numerical solution technique for second-order partial
differential equations on irregular grids.  It is designed
for applications where the physical quantities of interest
include derivatives of the the variable present in the
partial differential equation (PDE).  For example, a simple
model for flow in porous media is the so-called pressure
equation, a second order PDE, which describes the pressure
of a fluid in an underground reservoir.  In addition to the
pressure, one is often interested in the flow velocity of
the fluid which is related to derivatives of the pressure.

The discretization technique is closely related to two other
commonly used methods : control volume methods and mixed
finite element methods.  First, as in control volume methods,
we partition the domain into volumes and integrate the
continuous equations over each volume.  Then, as in mixed
finite element methods, we replace the continuous variables
by their discrete finite element approximations.  Numerical
results which illustrate the method's advantages over 
standard approaches will be included in the talk.

In getting a numerical solution for a problem generating the
discrete system from the continuous model (the PDE) is only
part of the work.  One must also solve the discrete system.
We have developed, more or less concurrently with the
discretization, two multilevel solvers.  The first is a
multigrid algorithm based on the CVMFE discretization on a
sequence of grids, and the second exploits the discretization's
connection to standard finite difference methods.  Numerical
results for both solvers are presented to illustrate their
advantages and limitations.