On the finite element approximation of infinity-harmonic functions
arXiv:1511.0047112 citationsh-index: 2
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This provides a rigorous justification for using finite element methods to approximate infinity-harmonic functions, which are important in optimal transport and image processing, but the result is incremental as it extends known convergence properties.
The authors prove that conforming Galerkin approximations of p-harmonic functions converge to infinity-harmonic functions as both p and the discretization parameter h approach zero, establishing a theoretical link between the two families of functions.
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.