Ralf Kornhuber Monotone

Monotone Iterations for Eliptic Variational Inequalities

Monotone Multigrid Methods for Elliptic Variational Inequalities I

We derive fast solvers for discrete elliptic variational inequalities of the rst kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear nite elements. Using basic ideas of successive subspace correction, we modify well-known relaxation methods by extending the set of search directions. Extended underrelaxations are called monotone multigr...

On Monotone Multigrid Methods for the Signorini Problem

SUMMARY Using well{known concepts from the scalar case (cf. Kor94]) we derive globally convergent multigrid methods for the discretized Signorini problem in linear elasticity. Special care has to be taken in case of varying normal directions. The algorithm can be implemented as a multigrid V{cycle with optimal complexity. In numerical experiments we observed similar convergence rates as for lin...

Adaptive Monotone Multigrid Methods for some Non{Smooth Optimization Problems

We consider the fast solution of non{smooth optimization problems as resulting for example from the approximation of elliptic free boundary problems of obstacle or Stefan type. Combining well{known concepts of successive subspace correction methods with convex analysis, we derive a new class of multigrid methods which are globally convergent and have logarithmic bounds of the asymptotic converg...

Monotone Multigrid Methods for Elliptic Variational Inequalities I 1

We derive fast solvers for discrete elliptic variational inequalities of the rst kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear nite elements. Using basic ideas of successive subspace correction, we modify well{known relaxation methods by extending the set of search directions. Extended under-relaxations are called monotone multig...