Computational quasi-reversibility method for Cauchy problems for Laplace's equation

Michael V. Klibanov; Fadil Santosa

doi:10.1137/0151085

Computational quasi-reversibility method for Cauchy problems for Laplace's equation

Michael V. Klibanov, Fadil Santosa

School of Mathematics

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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.

Original language	English (US)
Pages (from-to)	1653-1675
Number of pages	23
Journal	SIAM Journal on Applied Mathematics
Volume	51
Issue number	6
DOIs	https://doi.org/10.1137/0151085
State	Published - Jan 1 1991

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Computational quasi-reversibility method for Cauchy problems for Laplace's equation

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