Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers

Multilevel preconditioning - Appending boundary conditions by Lagrange multipliers

For saddle point problems stemming from appending essential boundary conditions in connection with Galerkin methods for elliptic boundary value problems, a class of multilevel preconditioners is developed. The estimates are based on the characterization of Sobolev spaces on the underlying domain and its boundary in terms of weighted sequence norms relative to corresponding multilevel expansions...

Appending boundary conditions by Lagrange multipliers: Analysis of the LBB condition

This paper is concerned with the analysis of discretization schemes for second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of Lagrange multipliers. Speciically, we show how the validity of the Lady senskaja{Babu ska{Brezzi (LBB) condition for the corresponding saddle point problems depends on the various ingredients of the involved discret...

Substructuring by Lagrange Multipliers

Appending Boundary Conditions by Lagrange Multipliers: General Criteria for the Lbb Condition

This paper is concerned with the analysis of discretization schemes for second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of Lagrange multipliers. Speciically, we show how the validity of the Lady senskaja{Babu ska{Brezzi (LBB) condition for the corresponding saddle point problems depends on the various ingredients of the involved discret...

Local Stability Conditions for the Babuska Method of Lagrange Multipliers

We consider the so-called Babuska method of finite elements with Lagrange multipliers for numerically solving the problem Au = f in il, u = g on 3Í2, iî C Rn, 7i > 2. We state a number of local conditions from which we prove the uniform stability of the Lagrange multiplier method in terms of a weighted, mesh-dependent norm. The stability conditions given weaken the conditions known so far and a...