On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates

DOI10.1051/m2an/2019073zbMath1440.35042arXiv1906.08700OpenAlexW2980339648MaRDI QIDQ5110271

Lucas Chesnel, Laurent Bourgeois

Publication date: 18 May 2020

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.08700

zbMATH Keywords

regularityCauchy problemfinite element methodsquasi-reversibilitycorners

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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The Morozov’s principle applied to data assimilation problems ⋮ Least squares solvers for ill-posed PDEs that are conditionally stable ⋮ Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method ⋮ Uniqueness' failure for the finite element Cauchy-Poisson's problem ⋮ Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations ⋮ On numerical resolution of an inverse Cauchy problem modeling the airflow in the bronchial tree ⋮ Full Discretization of Cauchy's Problem by Lavrentiev--Finite Element Method

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