2020/12/03 by Xu Li, Li, Xu, Hongxing Rui +1 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2012.01689
openalex publication_date 2020/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a P1c⊕ RT0-P0 discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity approximation with optimal order. Our method has the following features. Firstly, the global number of the degrees of freedom of our method is the same as the low order Bernardi and Raugel (B-R) finite element method (Bernardi and Raugel, 1985), while the number of the non-zero entries of the former is about half of the latter in the velocity-velocity region of the coefficient matrix. Secondly, the P1c component of the velocity, the RT0 component of the velocity and the pressure seem to solve a popular P1c-RT0-P0 discretization of a poroelastic-type system formally. Finally, our method can be easily transformed into a pressure-robust and stabilized P1c-P0 discretization for the Stokes problem via the static condensation of the RT0 component, which has a much smaller number of global degrees of freedom. Numerical experiments illustrating the robustness of our method are also provided.