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- Volker John
- Lecture Notes in Computational Science and…
- 2004

- Volker John, William J. Layton
- SIAM J. Numerical Analysis
- 2002

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, 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)

- Volker John, Songül Kaya
- Adv. Comput. Math.
- 2008

- Volker John
- LSSC
- 1997

- Volker John
- 2001

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)

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)

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)

- Volker John, Songül Kaya
- SIAM J. Scientific Computing
- 2005

This paper presents a variational multiscale method (VMS) for the incompressible Navier–Stokes equations which is defined by a large scale space L H for the velocity deformation tensor and a turbulent viscosity ν T. The connection of this method to the standard formulation of a VMS is explained. The conditions on L H under which the VMS can be implemented… (More)