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. (email@example.com)
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