Iterative solution methods
Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space
SIAM Journal on Numerical Analysis
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In this paper preconditioning is developed for mixed nonlinear elliptic boundary value problems using Sobolev space background. The approach generalizes the similar results of the authors for Dirichlet problems. Namely, a linear preconditioning operator is found first for the BVP itself on the continuous level, then the projection of this operator under the applied discretization will provide a natural preconditioning matrix. The mixed boundary conditions are incorporated in the preconditioner such that the derivative of the original boundary conditions is associated to the preconditioning operator. The paper first provides the theoretical foundation, then the construction and advantages of the proposed preconditioners are presented.