Wavelet Techniques for the Fictitious-Domain-Lagrange-Multiplier-Approach

We consider second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of Lagrange multipliers. This is combined with a fictitious domain approach into which the physical domain is embedded. The resulting saddle point problem will be discretized in ter...

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Bibliographic Details
Published in:Numerical algorithms 2001-07, Vol.27 (3), p.291-316
Main Author: Kunoth, Angela
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Discretization
Iterative methods
Iterative solution
Lagrange multiplier
Saddle points
Uzawa's algorithm
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Summary:We consider second order elliptic boundary value problems when essential boundary conditions are enforced with the aid of Lagrange multipliers. This is combined with a fictitious domain approach into which the physical domain is embedded. The resulting saddle point problem will be discretized in terms of wavelets, resulting in an operator equation in ℓ2. Stability of the discretization and consequently the uniform boundedness of the condition number of the finite-dimensional operator independent of the discretization is guaranteed by an appropriate LBB condition. For the iterative solution of the saddle point system, an incomplete Uzawa algorithm is employed. It can be shown that the iterative scheme combined with a nested iteration strategy is asymptotically optimal in the sense that it provides the solution up to discretization error on discretization level J in an overall amount of iterations of order O(NJ), where NJ is the number of unknowns on level J. Finally, numerical results are provided.
ISSN:1017-1398
1572-9265
DOI:10.1023/A:1011891106124