-convergence of saddle-point approximations for second order problems
Lagrangian approximations and weak solutions of the Navier-Stokes equations
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid....
Large norm solutions to nonlinear elliptic problems
Line Method Approximations to the Cauchy Problem for Nonlinear Parabolic Differential Equations.
Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
For robust discretizations of the Navier-Stokes equations with small viscosity, standard Galerkin schemes have to be augmented by stabilization terms due to the indefinite convective terms and due to a possible lost of a discrete inf-sup condition. For optimal control problems for fluids such stabilization have in general an undesired effect in the sense that optimization and discretization do not commute. This is the case for the combination of streamline upwind Petrov-Galerkin (SUPG) and pressure...
Local existence of classical solutions to the well-posed Hele-Shaw problem.
Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Long-Range and Periodic Solutions of Parabolic Problems.
Lösung der Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.