A Relaxed Kačanov iteration for the p-poisson problem

L. Diening, M. Fornasier, R. Tomasi, M. Wank

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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⩽ 2 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.

Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalNumerische Mathematik
Volume145
Issue number1
DOIs
StatePublished - 1 May 2020

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