A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates
Marián Slodička · The ANZIAM Journal · 2005
Abstract We consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ 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 (Ω), H 1 (Ω) and L ∞ (Ω) spaces under the minimal regularity assumptions of the exact solution.