A two-level subgrid stabilized Oseen iterative method for the steady Navier–Stokes equations

A Two‐Parameter Stabilized Finite Element Method for Incompressible Flows

“…What is worse, the iterative method used for solving the nonlinear system may fail to converge, and hence cannot yield an approximate solution at all (cf. ). As a result, stabilization methods are essential in simulations of high Reynolds number flows.…”

“…), the stabilization term in this method is based on an elliptic projector which projects higher‐order finite element interpolants of the velocity into a lower‐order finite element interpolation space defined on the same mesh as that for the discretization of the Navier–Stokes equations, and thus, only one single mesh is needed in computations. This method was subsequently combined with the two‐grid methods and the domain decomposition methods . Numerical tests illustrated the effectiveness and efficiency of this type of subgrid stabilized methods.…”

“…The significant feature of this combined method is that, it is able to simulate high Reynolds number flows without spurious oscillations compared with the standard two‐grid methods; when compared with the usual subgrid model methods, it can save a large amount of computational time. This work can be considered as a sequel of the paper . In , the numerical scheme on the fine grid is one step of the standard Newton iteration without any stabilizations, while here the linearized numerical form of the Navier–Stokes equations on the fine grid is stabilized and two stabilization approaches are considered and compared.…”

A parallel finite element variational multiscale method based on fully overlapping domain decomposition for incompressible flows

“…If the mesh scale is not small enough, spurious oscillations may occur in numerical simulation. What is worse, the iterative methods used to solve the nonlinear system may fail to converge and, consequently, cannot yield a solution at all (cf., [22][23][24]). For the above mentioned discretization approach based on fully overlapping decomposition, due to the coarseness of the mesh away from the interested subdomain, it is challenging to simulate high Reynolds number flows.…”

Error analysis of a fully discrete finite element variational multiscale method for time‐dependent incompressible Navier–Stokes equations

“…There are many stabilized methods for the simulation of high Reynolds number flows in literature, for example, the artificial viscosity method [9], the defect-correction methods [10][11][12][13][14], the subgrid stabilization methods [15][16][17][18][19][20][21][22], and the variational multiscale methods [23][24][25][26][27], among others. The artificial viscosity method adds an artificial viscosity to the inverse Reynolds number as a stability factor.…”