Relaxed Kacanov scheme for the p-Laplacian with large p

TL;DR

This paper presents a globally convergent relaxed Kacanov scheme for efficiently computing solutions to the p-Laplace problem for large p, with mesh-independent convergence rates and simple implementation.

Contribution

It introduces a novel, easy-to-implement iterative scheme that guarantees convergence without line searches or unknown parameters for the p-Laplace problem.

Findings

Scheme converges globally for all p ≥ 2.

Each iteration involves solving a weighted linear Poisson problem.

Convergence rate is independent of mesh size.

Abstract

We introduce a globally convergent relaxed Kacanov scheme for the computation of the discrete minimizer to the $p$-Laplace problem with $2 \leq p < \infty$. The iterative scheme is easy to implement since each iterate results only from the solve of a weighted, linear Poisson problem. It neither requires an additional line search nor involves unknown constants for the step length. The rate of convergence is independent of the underlying mesh.