A variational method and approximations of a Cauchy problem for elliptic equations

Dinh Nho Hào, B.T. Johansson, D. Lesnic, Pham Minh Hien

Research output: Contribution to journalArticle

Abstract

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Original languageEnglish
Pages (from-to)89-120
Number of pages32
JournalJournal of Algorithms and Computational Technology
Volume4
Issue number1
Early online date16 Feb 2010
DOIs
Publication statusPublished - Mar 2010

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