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A robust linearisation scheme for a nonlinear elliptic boundary value problem: Error estimates
Published online by Cambridge University Press: 17 February 2009
Abstract
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We consider a nonlinear second-order elliptic boundary value problem in a bounded domain Ω ⊂ RN 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 L2(Ω), H1(Ω) and L∞(Ω) spaces under the minimal regularity assumptions of the exact solution.
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