A relaxed Kačanov iteration for the \(p\)-Poisson problem. (English) Zbl 1442.65362
Summary: 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 \(1 < p \leq 2\) 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.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35D30 | Weak solutions to PDEs |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
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