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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
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.
- 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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