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Error estimates of an efficient linearization scheme for anonlinear elliptic problem with a nonlocal boundary condition

Published online by Cambridge University Press:  15 April 2002

Marian Slodička
Marian Slodička*
Affiliation:
Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, B-9000 Ghent, Belgium. (ms@cage.rug.ac.be)
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Abstract

We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain $\Omega\subset {\mathbb R}^N$ with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γn. The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization algorithm are derived in L2(Ω),H1(Ω) and L∞(Ω) spaces.

Keywords

Nonlinear elliptic BVPerror estimatesnonstandard boundary conditionlinearization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 691 - 711
Copyright
© EDP Sciences, SMAI, 2001

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