A pressure-robust divergence free finite element basis for the Stokes equations - Jay Chu; Xiaozhe Hu; Lin Mu (Electronic Research Archive)
This paper considered divergence-free basis methods to solve the viscous Stokes equations. A discrete divergence-free subspace was constructed to reduce the saddle point problem of the Stokes problem to a smaller-sized symmetric and positive definite system solely depending on the velocity components. Then, the system could decouple the unknowns in velocity and pressure and solve them independently. However, such a scheme may not ensure an accurate numerical solution to the velocity. In order to obtain satisfactory accuracy, we used a velocity reconstruction technique to enhance the divergence-free scheme to achieve the desired pressure and viscosity robustness. Numerical results were presented to demonstrate the robustness and accuracy of this discrete divergence-free method.