Analysis of a velocity–pressure–pseudostress formulation for the stationary Stokes equations ☆
By Gabriel N. Gatica, Antonio Márquez, Manuel A. Sánchez. 2010
108 citations recorded by the source corpus.
Abstract We consider a non-standard mixed approach for the Stokes problem in which the velocity, the pressure, and the pseudostress are the main unknowns. Alternatively, the pressure can be eliminated from the original equations, thus yielding an equivalent formulation with only two unknowns. In this paper we develop a priori and a posteriori error analyses of both approaches. We first apply the Babuska–Brezzi theory to prove the well-posedness of the continuous and discrete formulations. In particular, we show that Raviart–Thomas elements of order k ⩾ 0 for the pseudostresses, and piecewise polynomials of degree k for the velocities and the pressures, ensure unique solvability and stability of the associated Galerkin schemes. Then, we derive reliable and efficient residual-based a posteriori error estimators for both schemes, without and with pressure unknown. Finally, we provide several numerical results illustrating the good performance of the resulting mixed finite element methods, confirming the theoretical properties of the estimators, and showing the behaviour of the associated adaptive algorithms.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Geophysics
View Paper: https://www.semanticscholar.org/paper/a2b94c0513e9d2e8195a3e74c96ef3dd68c454b2
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In Computational Mechanics
In Computational Theory and Mathematics
In Geophysics
Citations in the corpus
- An augmented velocity–vorticity–pressure formulation for the Brinkman equations (2015, methodology): “In the former, the approach from [7] (see also [8]) is adapted to propose an augmented mixed method in terms of velocity and pseudostress, for which optimal error estimates are proved.”