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A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates

Published online by Cambridge University Press:  17 February 2009

Marian Slodička
Marian Slodička
Affiliation:
Department of Mathematical Analysis, Ghent University, Galglaan 2, B-9000 Gent, Belgium; e-mail: marian.slodicka@ugent.be.
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Abstract

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We consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005 , pp. 449 - 470
Copyright
Copyright © Australian Mathematical Society 2005

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