2024/12/12 by Michael Neilan, Neilan, Michael, Haiyan Wan +1 · 2 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics Simulations and Interactions
paper · pdf · doi:10.48550/arxiv.2412.09689
We propose a C0 interior penalty method for the fourth-order stream\nfunction formulation of the surface Stokes problem. The scheme utilizes\ncontinuous, piecewise polynomial spaces defined on an approximate surface. We\nshow that the resulting discretization is positive definite and derive error\nestimates in various norms in terms of the polynomial degree of the finite\nelement space as well as the polynomial degree to define the geometry\napproximation. A notable feature of the scheme is that it does not explicitly\ndepend on the Gauss curvature of the surface. This is achieved via a novel\nintegration-by-parts formula for the surface biharmonic operator.\n