This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles and is pressure-robust in the small viscosity regime. For the Stokes problem, an error estimate uniform with respect to the kinematic viscosity is shown. For the Navier--Stokes equation, the nonlinear convection term is discretized using an edge-averaged finite element method. In comparison with classical schemes, the proposed method does not require tuning of parameters and is validated for competitiveness on several benchmark problems in 2 and 3 dimensional space.
Application of Stabilized Explicit Runge-Kutta Methods to the Incompressible Navier-Stokes Equations by means of a Projection Method and a Differential Algebraic Approach
Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes equations with variable density and artificial compressibility
Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier-Stokes equations
Skeleton-stabilized ImmersoGeometric Analysis for incompressible viscous flow problems
Eindhoven University of Technology（埃因霍温理工大学）；IUSS – Istituto Universitario di Studi Superiori Pavia（帕维亚高等大学研究院）；University of Pavia（帕维亚大学）；Utrecht University（乌得勒支大学）
A structure-preserving integrator for incompressible finite elastodynamics based on a grad-div stabilized mixed formulation with particular emphasis on stretch-based material models
Data assimilation in 2D incompressible Navier-Stokes equations, using a stabilized explicit $O(Δt)^2$ leapfrog finite difference scheme run backward in time
A Volumetrically Stabilized Mixed Formulation of the Finite Element Immersed Boundary Method for Fluid Structure Interaction with Fully Incompressible Hyperelastic Solids
University at Buffalo（布法罗大学）；Advanced Micro Devices, Inc.（超威半导体公司）
A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization
University of Nebraska-Lincoln（内布拉斯加大学林肯分校）；Los Alamos National Lab（洛斯阿拉莫斯国家实验室）；Texas A&M University（德克萨斯农工大学）；Weizmann Institute of Science（魏茨曼科学研究所）；University of Exeter（埃克塞特大学）
Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance
IE School of Science and Technology, IE University（IE科学与技术学院，IE大学）；Department of Mathematics, University of Michigan（密歇根大学数学系）；Centre for Automation and Robotics (CSIC-UPM)（自动化与机器人中心（西班牙国家研究委员会-马德里理工大学））
A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics
Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile（圣地亚哥智利大学计算热与流体流动实验室）；Department of Mechanical Engineering, University of Santiago de Chile（圣地亚哥智利大学机械工程系）；Chair for Computational Analysis of Technical Systems, RWTH Aachen University（亚琛工业大学技术系统计算分析教席）；Chair of Methods for Model-based Development in Computational Engineering, RWTH（亚琛工业大学计算工程基于模型开发方法教席）；Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University（亚琛工业大学仿真与数据科学中心（JARA-CSD））
