A low-degree strictly conservative finite element method for incompressible flows on general triangulations

Zeng, Huilan; Zhang, Chen-Song; Zhang, Shuo

The SMAI Journal of computational mathematics, Tome 8 (2022), pp. 225-248.

In this study, a new $P_2-P_1$ finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn’s inequality hold for general triangulations. It yields strictly conservative velocity approximations when applied to models of incompressible flows. The convergence rate of the scheme can only be proved to be of suboptimal $𝒪\left(h\right)$ order, though, based on the property of strict conservation, the robust capacity of the pair for incompressible flows is verified theoretically and numerically.

Classification : 65N12, 65N30, 76D05
Mots clés : incompressible (Navier–)Stokes equations, Brinkman equations, inf-sup condition, discrete Korn’s inequality, strictly conservative scheme, pressure-robust discretization

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