Meshfree finite difference approximations for functions of the eigenvalues of the Hessian

Document Type

Article

Publication Date

1-1-2018

Abstract

We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. Approximations are defined on unstructured point clouds, which allows for very complicated domains and a non-uniform distribution of discretisation points. The schemes are monotone, which ensures that they converge to the viscosity solution of the underlying PDE as long as the equation has a comparison principle. Numerical experiments demonstrate convergence for a variety of equations including problems posed on random point clouds, complex domains, degenerate equations, and singular solutions.

Identifier

85020743232 (Scopus)

Publication Title

Numerische Mathematik

External Full Text Location

https://doi.org/10.1007/s00211-017-0898-2

ISSN

0029599X

First Page

75

Last Page

99

Issue

1

Volume

138

Grant

1619807

Fund Ref

National Science Foundation

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