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

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

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

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

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.