ON THE SOLUTION OF THE DIRICHLET PROBLEM FOR LINEAR ELLIPTIC-OPERATORS BY A DISTRIBUTED LAGRANGE MULTIPLIER METHOD

In this Note we discuss the construction of efficient preconditioners for the solution of finite-dimensional saddle-point problems. A partic ular attention is given to those linear systems associated to the solu tion of elliptic problems by methods combining fictitious domain and d istributed Lagrange multiplier techniques to force boundary conditions . It is shown that with the approach discussed in this Note we can con struct preconditioners spectrally equivalent to the original saddle-po int matrix and leading to algorithms of optimal arithmetic complexity. (C) Academie des Sciences/Elsevier, Paris.