On Schwarz-type smoothers for saddle point problems with applications to PDE-constrained optimization problems
The authors consider multigrid methods for solving large-scale systems of discretized mixed variational problems of the form \[ \text{Find }x\in X\text{ and }p\in Q\text{ such that }a(x,w)+ b(w,p)=\langle F,w\rangle\text{ for all }w\in X, \] \[ b(x,q)- c(p,q)= \langle G,q\rangle\text{ for all }q\in Q. \] The main applications considered in the paper are optimization problems in function spaces with constraints in form of partial differential equations. Some numerical experiments are given.
scientific article; zbMATH DE number 5503888
scientific article