Numerical methods for the 2-Hessian elliptic partial differential equation

Document Type

Article

Publication Date

1-1-2017

Abstract

The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three-dimensional manifolds. We ntroduce two numerical methods for this PDE: the first is provably convergent to the viscosity solution and the second is more accurate and convergent in practice but lacks a proof. The PDE is elliptic on a restricted set of functions: a convexity-type constraint is needed for the ellipticity of the PDE operator. Solutions with both iscretizations are obtained using Newton's method. Computational results are presented on a number of exact solutions which range in regularity from mooth to nondifferentiable and in shape from convex to nonconvex.

Identifier

85020924696 (Scopus)

Publication Title

IMA Journal of Numerical Analysis

External Full Text Location

https://doi.org/10.1093/imanum/drw007

e-ISSN

14643642

ISSN

02724979

First Page

209

Last Page

236

Issue

1

Volume

37

Grant

SFRH/BD/84041/2012

Fund Ref

Fundação para a Ciência e a Tecnologia

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