返回Google圖書搜尋

Pressure-robustness and Discrete Helmholtz Projectors in Mixed Finite Element Methods for the Incompressible Navier-Stokes Equations

出版	Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016
URL	http://books.google.com.hk/books?id=BJL-uQEACAAJ&hl=&source=gbs_api

註釋Recently, it was understood how to repair a certain L2-orthogonality of discretely-divergence-free vector fields and gradient fields such that the velocity error of inf-sup stable discretizations for the incompressible Stokes equations becomes pressure-independent. These new 'pressure-robust' Stokes discretizations deliver a small velocity error, whenever the continuous velocity field can be well approximated on a given grid. On the contrary, classical inf-sup stable Stokes discretizations can guarantee a small velocity error only, when both the velocity and the pressure field can be approximated well, simultaneously. In this contribution, 'pressure-robustness' is extended to the time-dependent Navier-Stokes equations. In particular, steady and time-dependent potential flows are shown to build an entire class of benchmarks, where pressure-robust discretizations can outperform classical approaches significantly. Speedups will be explained by a new theoretical concept, the 'discrete Helmholtz projector' of an inf-sup stable discretization. Moreover, different discrete nonlinear convection terms are discussed, and skew-symmetric pressure-robust discretizations are proposed.