On the convergence of iterated penalty methods for structure-preserving discretizations of saddle point problems
For researchers using structure-preserving discretizations, this work offers improved theoretical understanding of iterated penalty methods, though the results are incremental.
The paper provides new convergence estimates for iterated penalty methods applied to structure-preserving discretizations of saddle point problems, with sharper stability estimates for penalized systems. Three finite element applications confirm the theoretical results.
We present new convergence estimates for the iterated penalty method applied to structure-preserving discretizations of linear generalized saddle point systems. The method may be viewed as an Uzawa iteration on an augmented Lagrangian formulation of the system. As a by-product, we obtain sharper stability estimates for penalized/perturbed saddle point problems. Three model finite element applications show agreement with the theory.