Recent Advances on a Stable Hybrid Finite Elements Methodology for Stokes Flow using H(div) Spaces
Resumen
The motion of an incompressible flow can be accurately described by the Navier-Stokes equations. When the viscous forces have a greater influence compared to the convective ones, eg: creeping flows, the governing equations can be simplified to the linear Stokes equations. Moreover, the flow is said to be in a steady state if the magnitude of the inertial forces is much smaller than the other terms, thus not varying its velocity in time. [...]
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Denise De Siqueira, Phillipe RB Devloo, and Sônia M Gomes. “A new procedure for the construction of hierarchical high order Hdiv and Hcurl finite element spaces”. In: Journal of Computational and Applied Mathematics 240 (2013), pp. 204–214.
Pablo GS Carvalho, Philippe RB Devloo, and Sônia M Gomes. “On the use of divergence balanced H (div)-L2 pair of approximation spaces for divergence-free and robust simulations of Stokes, coupled Stokes–Darcy and Brinkman problems”. In: Mathematics and Computers in Simulation 170 (2020), pp. 51–78.
Philippe RB Devloo, Jeferson WD Fernandes, Sônia M Gomes, Francisco T Orlandini, and Nathan Shauer. “An efficient construction of divergence-free spaces in the context of exact finite element de Rham sequences”. In: Computer Methods in Applied Mechanics and Engineering 402 (2022), p. 115476.
