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A Dual-Mixed Approximation Method for a Three-Field Model of
a\\
 Nonlinear Generalized Stokes Problem

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V. J. Ervin\\
Department of Mathwmatical Sciences\\
Clemson University\\
Clemson, SC  19634-0975\\
vjarvin@clemson.edu\\

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J. S. Howell\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA  15213\\
howell4@andrew.cmu.edu\\

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I. Stanculescu\\
Department of Mathematics\\
University of Pittsburgh\\
Pittsburgh, PA  15260\\
ius1@pitt.edu\\

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\noindent {\bf Abstract}: In this work a dual-mixed approximation of a
nonlinear generalized Stokes problem is studied.  The problem is analyzed in
Sobolev spaces which arise naturally in the problem formulation. Existence and
uniqueness results are given and error estimates are derived.  It is shown
that both lowest-order and higher-order mixed finite elements are suitable for
the approximation method.  Numerical experiments that support the theoretical
results are presented.


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