Lutz Tobiska

A Two-Level Method with Backtracking for the Navier--Stokes Equations

We consider a two-level method for resolving the nonlinearity in finite element approximations of the equilibrium Navier--Stokes equations. The method yields L2 and H1 optimal velocity approximations and an L2 optimal pressure approximation. The two-level method involves solving one small, nonlinear coarse mesh system, one Oseen problem (hence, linear with positive definite symmetric part) on the fine mesh, and one linear correction problem on the coarse mesh. The algorithm we study produces an approximate solution with the optimal, asymptotic in h, accuracy for any fixed Reynolds number. We do not consider the behavior of the error for fixed h as

Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations

Re\rightarrow \infty

The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy

, i.e., for flows in transition to turbulence.

A finite difference analysis of a streamline diffusion method on a Shishkin mesh

For the Stokes equations with convection and the incompressible Navier–Stokes equations, the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure, thus allowing the use of arbitrary pairs of velocity-pressure spaces. For the linear problem, the authors obtain for all mesh–Peclet numbers optimal error estimates in natural norms including, in particular, the

The inf-sup condition for the mapped Q k - P k-1 disc element in arbitrary space dimensions

L^2

Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier–Stokes equations

-norm of the pressure. The same holds for the nonlinear problem, which close to a regular branch of solutions, i.e., the linearized operator, is an isomorphism of the norm of the inverse of which still depends on the Reynolds number. Consequently, the dependence of the error constants on the Reynolds number is not completely resolved in this case.

LOCAL PROJECTION STABILIZATION OF EQUAL ORDER INTERPOLATION APPLIED TO THE STOKES PROBLEM

The streamline-diffusion finite element method (SDFEM) is applied to a convection-diffusion problem posed on the unit square, using a Shishkin rectangular mesh with piecewise bilinear trial functions. The hypotheses of the problem exclude interior layers but allow exponential boundary layers. An error bound is proved for

The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation

\|u^I-u^N\|_{SD}

A Numerical Study of a Class of LES Models

, where

A coupled arbitrary Lagrangian-Eulerian and Lagrangian method for computation of free surface flows with insoluble surfactants

u^I