A Finite Element Method for Inhomogeneous Problems
          Using a Multigrid Algorithm for Eliminating the Boundary 
                                  Condition

                               Dana M. Bedivan

         Department of Mathematics, University of Texas at Arlington
                    BOX 19408, Arlington, TX 76019, U.S.A.

                                   Abstract

A finite element method is used for discretizing an elliptic problem with
inhomogeneous essential boundary conditions posed on a bounded convex
polyhedral domain.  The approximation of the inhomogeneous boundary condition
is made by a projection of the the given data on a finite dimensional space.
The error analysis shows that using a multigrid algorithm for finding the
approximating projection and eliminating the boundary condition does not
affect the optimal error rate for the finite element solution of the problem.
Sample computations are provided.