On the finite element approximation of infinity-harmonic functions

TL;DR

This paper demonstrates that conforming Galerkin methods for p-harmonic functions converge to infinity-harmonic functions as p approaches infinity and the discretization parameter h approaches zero.

Contribution

It establishes the convergence of finite element approximations for p-harmonic functions to infinity-harmonic functions in the simultaneous limit of p to infinity and h to zero.

Findings

Conforming Galerkin approximations tend to infinity-harmonic functions as p→∞ and h→0.

The paper provides a theoretical foundation for numerical approximation of infinity-harmonic functions.

Convergence results are proved under specific discretization conditions.

Abstract

In this note we show that conforming Galerkin approximations for p-harmonic functions tend to infinity-harmonic functions in the limit p \to \infty and h \to 0, where h denotes the Galerkin discretisation parameter.