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On the finite-element approximation of ∞-harmonic functions

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  30 January 2018

Tristan Pryer
Tristan Pryer*
Affiliation:
Department of Mathematics and Statistics, Whiteknights, University of Reading, Reading RG6 6AX, UK (t.pryer@reading.ac.uk)
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Abstract

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In this paper we show that conforming Galerkin approximations for p-harmonic functions tend to ∞-harmonic functions in the limit p → ∞ and h → 0, where h denotes the Galerkin discretization parameter.

Keywords

Galerkin methods∞-Laplacianviscosity solutions

MSC classification

Secondary: 65N12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 819 - 834
Copyright
Copyright © Royal Society of Edinburgh 2018