Sobolev Space Preconditioning for Mixed Nonlinear Elliptic Boundary Value Problems
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems
Computers & Mathematics with Applications
Preconditioning operators and Sobolevgradients for nonlinear elliptic problems
Computers & Mathematics with Applications
Nonlinear least squares and Sobolev gradients
Applied Numerical Mathematics
Computers & Mathematics with Applications
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The aim of this paper is to develop stepwise variable preconditioning for the iterative solution of monotone operator equations in Hilbert space and apply it to nonlinear elliptic problems. The paper is built up to reflect the common character of preconditioned simple iterations and quasi-Newton methods. The main feature of the results is that the preconditioners are chosen via spectral equivalence. The latter can be executed in the corresponding Sobolev space in the case of elliptic problems, which helps both the construction and convergence analysis of preconditioners. This is illustrated by an example of a preconditioner using suitable domain decomposition.