
A Mann iterative regularization method for elliptic Cauchy problems
We investigate the Cauchy problem for linear elliptic operators with C^∞...
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On level set type methods for elliptic Cauchy problems
Two methods of level set type are proposed for solving the Cauchy proble...
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On iterative methods for solving illposed problems modeled by PDE's
We investigate the iterative methods proposed by Maz'ya and Kozlov (see ...
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On inverse problems modeled by PDE's
We investigate the iterative methods proposed by Maz'ya and Kozlov (see ...
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An efficient algorithm for solving elliptic problems on percolation clusters
We present an efficient algorithm to solve elliptic Dirichlet problems d...
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BiParametric Operator Preconditioning
We extend the general operator preconditioning framework [R. Hiptmair, C...
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Tensor numerical method for optimal control problems constrained by an elliptic operator with general rankstructured coefficients
We introduce tensor numerical techniques for solving optimal control pro...
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An iterative method for solving elliptic Cauchy problems
We investigate the Cauchy problem for elliptic operators with C^∞coefficients at a regular set Ω⊂ R^2, which is a classical example of an illposed problem. The Cauchy data are given at the subset Γ⊂∂Ω and our objective is to reconstruct the trace of the H^1(Ω) solution of an elliptic equation at ∂Ω / Γ. The method described here is a generalization of the algorithm developed by Maz'ya et al. [Ma] for the Laplace operator, who proposed a method based on solving successive wellposed mixed boundary value problems (BVP) using the given Cauchy data as part of the boundary data. We give an alternative convergence proof for the algorithm in the case we have a linear elliptic operator with C^∞coefficients. We also present some numerical experiments for a special non linear problem and the obtained results are very promisive.
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