A Relaxed Kačanov iteration for the p-poisson problem
Lars Diening, Massimo Fornasier, Roberto Tomasi, Maximilian Wank
Abstract
Abstract In this paper we introduce and analyze an iteratively re-weighted algorithm, that allows to approximate the weak solution of the p -Poisson problem for $$1 < p \leqslant 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo><</mml:mo><mml:mi>p</mml:mi><mml:mo>⩽</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> by iteratively solving a sequence of linear elliptic problems. The algorithm can be interpreted as a relaxed Kačanov iteration, as so-called in the specific literature of the numerical solution of quasi-linear equations. The main contribution of the paper is proving that the algorithm converges at least with an algebraic rate.