The authors acknowledge support from the Austrian Science Fund (FWF) through the research program “Taming complexity in partial differential systems” (F65)—project “Automated discretization in multiphysics” (P10), the research program W1245, and the NSF grants 1912779, 2136228.
Journal of Scientific Computing
Fluids -- Velocity and Vorticity, Incompressible Stokes equations · Mixed finite elements, Pressure-robustness, Hybrid discontinuous Galerkin methods, Discrete Korn inequality
We introduce two new lowest order methods, a mixed method, and a hybrid discontinuous Galerkin method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi–Douglas–Marini space for approximating the velocity and the lowest order Raviart–Thomas space for approximating the vorticity. Our methods are based on the physically correct viscous stress tensor of the fluid, involving the symmetric gradient of velocity (rather than the gradient), provide exactly divergence-free discrete velocity solutions, and optimal error estimates that are also pressure robust. We explain how the methods are constructed using the minimal number of coupling degrees of freedom per facet. The stability analysis of both methods are based on a Korn-like inequality for vector finite elements with continuous normal component. Numerical examples illustrate the theoretical findings and offer comparisons of condition numbers between the two new methods.
Copyright (c) 2023 The Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
Gopalakrishnan, J., Kogler, L., Lederer, P. L., & Schöberl, J. (2023). Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling. Journal of Scientific Computing, 95(3), 91.