The identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method. The minimization problem is then proved to be equivalent to the saddle-point problem of an augmented Lagrangian. The finite element method is used to discretize the saddle-point problem, and the convergence of th...

The paper is devoted to domain decomposition methods (DDM in short) for the 18 Stokes problem with the slip boundary conditions. The original domain is cut into 19 two sub-domains and the augmented Lagrangian formulation for separate resulting 20 Poisson problems in both domains is used for computations. To relate solutions of 21 these two sub-problems to the original solution, one has to intro...

Convergence analysis of a nested iterative scheme proposed by Bank,Welfert and Yserentant (BWY) ([Numer. Math., 666: 645-666, 1990]) for solving saddle point system is presented. It is shown that this scheme converges under weaker conditions: the contraction rate for solving the (1, 1) block matrix is bound by ( √ 5− 1)/2. Similar convergence result is also obtained for a class of inexact Uzawa...

In this article, the denoising of smooth (H1-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the convex, non-smooth optimization problems resulting from the denoising formulation. We describe the algorithm, discuss its convergence and present the results of numerical experiments, which validate the methods ...

Two new Gauge–Uzawa schemes are constructed for incompressible flows with variable density. One is in the conserved form while the other is in the convective form. It is shown that the first-order versions of both schemes, in their semi-discretized form, are unconditionally stable. Numerical experiments indicate that the first-order (resp. second-order) versions of the two schemes lead to first...

We consider robust iterative methods for discontinuous Galerkin (DG) H(div,Ω)conforming discretizations of the Brinkman equations. We describe a simple Uzawa iteration for the solution of this problem, which requires the solution of a nearly incompressible linear elasticity type equation with mass term on every iteration. We prove the uniform stability of the DG discretization for both problems...