A mixed finite element method for the Stokes problem: an accelerations-pressure formulation
Applied Mathematics and Computation
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
A Multigrid Method for the Pseudostress Formulation of Stokes Problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A-posteriori error analysis to the exterior Stokes problem
Applied Numerical Mathematics
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In this work a finite element method for a dual-mixed approximation of Stokes and nonlinear Stokes problems is studied. The dual-mixed structure, which yields a twofold saddle point problem, arises in a formulation of this problem through the introduction of unknown variables with relevant physical meaning. The method approximates the velocity, its gradient, and the total stress tensor, but avoids the explicit computation of the pressure, which can be recovered through a simple postprocessing technique. This method improves an existing approach for these problems and uses Raviart-Thomas elements and discontinuous piecewise polynomials for approximating the unknowns. Existence, uniqueness, and error results for the method are given, and numerical experiments that exhibit the reduced computational cost of this approach are presented.