Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier–Stokes equations

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SOLUTIONS OF 3D NAVIER-STOKES BENCHMARK PROBLEMS WITH ADAPTIVE FINITE ELEMENTS (2006, methodology): “Although the problem has been formulated a couple of years ago accurate reference solutions are only determined for the geometry with circular cross-section by John [ 12 ].”
Efficient augmented Lagrangian‐type preconditioning for the Oseen problem using Grad‐Div stabilization (2013, methodology): “Solving Oseen-type systems has a long history and there are dozens of different solution approaches ranging from Uzawa type methods [2] to projection methods [3], special multi-grid methods [4] or block saddle point preconditioners [5, 6, 7].”
An L2‐stable approximation of the Navier–Stokes convection operator for low‐order non‐conforming finite elements (2011, background): “The three computed characteristic quantities lie in the reference intervals given by the benchmark outcomes, even if the low degree of the approximation and the direct computation of the forces exerting on the cylinder do not allow an accuracy comparable to [24, 5].”
Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method (2006, background): “For overcoming this difficulty, a volume integration instead of the conventional surface integral for the calculation of the hydrodynamic forces by introducing an auxiliary function [4, 12] has been proposed.”