In the present contribution we propose a novel conforming Finite Element scheme for the time-dependent Navier-Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a "divergence-free" velocity/pressure couple (such as the Scott-Vogelius element), a Discontinuous Galerkin in time approximation, and a suitable SUPG-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.

翻译：本文针对时间依赖型Navier-Stokes方程提出了一种新的协调有限元格式，并证明了该格式同时具有对流拟鲁棒性与压力鲁棒性。该方法通过结合"散度自由"的流速/压力耦合对（如Scott-Vogelius单元）、时间方向上的间断Galerkin逼近以及适当的SUPG-curl稳定化技术构建而成。文中还包含了与理论结果相符的数值实验验证。