Nonconforming Finite Element Method Applied to the Driven Cavity Problem (Communications in Computational Physics, 2018)
A cheapest stable nonconforming finite element method is presented forsolving the incompressible flow in a square cavity without smoothing the corner singularities.The stable cheapest nonconforming finite element pair based on P1×P0 onrectangular meshes [29] is employed with a minimal modification of the discontinuousDirichlet data on the top boundary, where $\widetilde{\mathcal{P}^h_0}$ is the finite element space of piecewiseconstant pressures with the globally one-dimensional checker-board pattern subspaceeliminated. The proposed Stokes elements have the least number of degrees of freedomcompared to those of known stable Stokes elements. Three accuracy indicationsfor our elements are analyzed and numerically verified. Also, various numerous computationalresults obtained by using our proposed element show excellent accuracy.