A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation

1991/12/01 by Michael V. Klibanov, Fadil Santosa · 3 citations
Engineering · Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Heat Transfer and Mathematical Modeling

paper · doi:10.1137/0151085

crossref issued 1991/12/01 · crossref published 1991/12/01 · crossref published-print 1991/12/01 · openalex publication_date 1991/12/01 · crossref created 2005/02/23 · crossref deposited 2019/01/28 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31

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.

Cited by

• Constructing a variational quasi-reversibility method for a Cauchy problem for elliptic equations
• Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations
• Convexification method for a coefficient inverse problem and its performance for experimental backscatter data for buried targets