Volume 35, Number 4, July-August 2001
|Page(s)||691 - 711|
|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. (firstname.lastname@example.org)
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.