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- Volker John, Lutz Tobiska
- 1999

In recent benchmark computations 1], coupled multigrid methods have been proven as eecient solvers for the incompressible Navier{Stokes equations. We present a numerical study of two classes of smoothers in the framework of coupled multigrid methods. The class of Vanka{type smoothers is characterized by the solution of small local linear systems of… (More)

We present a numerical study of several nite element discretizations applied to a benchmark problem for the 2d steady state incompressible Navier{ Stokes equations deened in Schh afer and Turek (1996). The discretizations are compared with respect to the accuracy of the computed benchmark parameters. Higher order isoparametric nite element discretizations… (More)

We consider the question of \numerical errors" in large eddy simulation. It is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent ows with complexity independent of the Reynolds number and depending only on the resolution \" of the eddies sought. This… (More)

- Volker John
- 2002

We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier– Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for ÿnite element discretizations. Numerical tests on two-and three-dimensional channel ows across a step using the slip with friction boundary… (More)

- Volker John
- 1998

This paper presents a detailed numerical study of the parallel performance of coupled multigrid V{, F{, and W{cycle for the solution of the incompressible Navier{Stokes equations. The results show the considerable innuence of the number of processors on a good choice of components and parameters of the algorithms. Some general suggestions concerning this… (More)

- Volker John
- 2002

SUMMARY This paper presents a numerical study of the 3D ow around a cylinder which was deÿned as a benchmark problem for the steady state Navier–Stokes equations within the DFG high-priority research program ow simulation with high-performance computers by Sch afer and Turek (Vol. 52, Vieweg: Braunschweig, 1996). The ÿrst part of the study is a comparison… (More)

The paper studies finite element methods for the simulation of time–dependent convection–diffusion–reaction equations with small diffusion: the SUPG method, a SOLD method and two types of FEM– FCT methods. The methods are assessed, in particular with respect to the size of the spurious oscillations in the computed solutions, at a 3D example with… (More)

- Volker John, Songul Kaya, William Layton, Nsf Grant
- 2006

This paper studies the error in, the efficient implementation of and time stepping methods for a variational multiscale method (VMS) for solving convection-dominated problems. The VMS studied uses a fine mesh C 0 finite element space X h to approximate the concentration and a coarse mesh discontinuous vector finite element space L H for the large scales of… (More)