A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations
Abstract
In this paper, a well-posed simultaneous space-time first order system least squares formulation is constructed of the instationary incompressible Stokes equations with slip boundary conditions. As a consequence of this well-posedness, the minimization over any conforming triple of finite element spaces for velocities, pressure, and stress tensor gives a quasi-best approximation from that triple. The formulation is practical in the sense that all norms in the least squares functional can be efficiently evaluated. Being of least squares type, the formulation comes with an efficient and reliable a posteriori error estimator. In addition, a priori error estimates are derived, and numerical results are presented.
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© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 9 July 2021
Accepted: 21 March 2022
Published online: 30 June 2022
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Austrian Science Fund https://doi.org/10.13039/501100002428 : J4379-N
National Science Foundation https://doi.org/10.13039/100000001 : DMS-172029
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