A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
Michael V. Klibanov, Fadil Santosa
Source abstract
This work concerns the use of the method of quasi-reversibility for solving Cauchy problems for Laplace’s equation. The paper begins with a derivation of an error estimate for this method using Carleman’s estimates. Next, a discretization of the method using finite differences is considered. Carleman-type estimates for the discrete scheme are derived and used to establish convergence of the numerical method. Results of numerical experimentations with the method are presented.
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