Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems |
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Authors: | Ivo Babu?ka Jan Chleboun |
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Institution: | (1) TICAM, The University of Texas at Austin, TX 78713, USA; e-mail: babuska@mail.utexas.edu , US;(2) Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, Prague 115 67, Czech Republic; e-mail: chleb@math.cas.cz , CZ |
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Abstract: | Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with
Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains
and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem
can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists
in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz
and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation
is possible and can be done in different ways.
Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002
RID="*"
ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and
NSF DMS-9802367
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ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated |
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Keywords: | Mathematics Subject Classification (1991): 65N99 65N12 35J25 |
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