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arXiv · 1006.3319

Convergence of an adaptive Ka\v{c}anov FEM for quasi-linear problems

Eduardo M. Garau·Pedro Morin·Carlos Zuppa
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Abstract

We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is thus \emph{inexact} because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Ka\v{c}anov), using the approximation of the previous mesh as an initial guess. The convergence of the method is proved for any \emph{reasonable} marking strategy and starting from any initial mesh. We conclude with some numerical experiments that illustrate the theory.

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Eduardo M. Garau, Pedro Morin, Carlos Zuppa. 2010-06-16. Convergence of an adaptive Ka\v{c}anov FEM for quasi-linear problems. https://arxiv.org/abs/1006.3319

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