![]() ![]() Approximations are defined on unstructured point clouds, which allows for very complicated domains and a non-uniform distribution of discretisation points. Numerical experiments demonstrate convergence for a variety of equations including problems posed on random point clouds, complex domains, degenerate equations, and singular solutions.ĪB - We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. 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. N2 - We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. © 2017, Springer-Verlag GmbH Deutschland. This work was partially supported by NSF DMS-1619807. T1 - Meshfree finite difference approximations for functions of the eigenvalues of the Hessian ![]()
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