| Issue |
ESAIM: M2AN
Volume 35, Number 4, July-August 2001
|
|
|---|---|---|
| Page(s) | 691 - 711 | |
| DOI | https://doi.org/10.1051/m2an:2001132 | |
| Published online | 15 April 2002 | |
Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition
Department of Mathematical
Analysis, Faculty of Engineering, Ghent University, Galglaan 2,
B-9000 Ghent, Belgium. (ms@cage.rug.ac.be)
Received:
6
July
2000
Revised:
13
November
2000
We consider a nonlinear second order elliptic boundary
value problem (BVP)
in a bounded domain 
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.
Mathematics Subject Classification: 65N15 / 35J60
Key words: Nonlinear elliptic BVP / error estimates / nonstandard boundary condition / linearization.
© EDP Sciences, SMAI, 2001
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