ANZIAM  J.  46 (2005), 449-470
A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates

Marian Slodicka
  Department of Mathematical Analysis
  Ghent University
  Galglaan 2
  B-9000 Gent

We consider a nonlinear second-order elliptic boundary value problem in a bounded domain $\Omega \subset \mathbb{R}^N$ with mixed boundary conditions. The solution is found via linearisation. We design a robust and efficient approximation scheme. Error estimates for the linearisation algorithm are derived in $L_2(\Omega)$, $H^1(\Omega)$ and $L_{\infty}(\Omega)$ spaces under the minimal regularity assumptions of the exact solution.
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