Adaptive monotone multigrid methods for some non-smooth optimization problems
- Kornhuber, Ralf
2010 Mathematics Subject Classification
- 65N30 65N55 35J85
- free boundary problems, adaptive finite element methods, multigrid methods
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 convergence rates. The theoretical considerations are illustrated by numerical experiments.