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The method of quasi‐reversibility to solve the Cauchy problems for elliptic partial differential equations
Author(s) -
Bourgeois Laurent,
Lunéville Eric
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700001
Subject(s) - elliptic partial differential equation , cauchy distribution , computation , a priori and a posteriori , mathematics , cauchy problem , partial differential equation , operator (biology) , initial value problem , elliptic operator , mathematical analysis , algorithm , chemistry , philosophy , biochemistry , epistemology , repressor , transcription factor , gene
We use the method of quasi‐reversibility, first introduced in [1], to solve the ill‐posed Cauchy problems for an elliptic operator such as P = –Δ. In particular, a non‐conforming method is implemented, some a priori error estimates are derived, and a few numerical computations are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)