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

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)

Fluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are… (More)

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

- Volker John, Lutz Tobiska
- 2000

Coupled multigrid methods have been proven as eecient solvers for the incompressible Navier{ Stokes equations in recent benchmark computations ST96a]. This paper presents a numerical study of two classes of smoothers in these methods. The class of Vanka{type smoothers is characterized by the solution of small local linear systems of equations in a… (More)

- 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 /nite element discretizations. Numerical tests on twoand three-dimensional channel 2ows 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)

- 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, 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 LH for the velocity deformation tensor and a turbulent viscosity νT . The connection of this method to the standard formulation of a VMS is explained. The conditions on LH under which the VMS can be implemented… (More)

- Volker John, Petr Knobloch, Gunar Matthies, Lutz Tobiska
- Computing
- 2002

We consider a general framework for analysing the convergence of multi-grid solvers applied to finite element discretisations of mixed problems, both of conforming and nonconforming type. As a basic new feature, our approach allows to use different finite element discretisations on each level of the multi-grid hierarchy. Thus, in our multi-level approach,… (More)