NDLI: Vanishing Moment Method and Moment Solutions for Fully Nonlinear Second Order Partial Differential Equations

Content Provider	Springer Nature Link
Author	Feng, Xiaobing Neilan, Michael
Copyright Year	2008
Abstract	This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily computed by existing numerical methods such as finite difference, finite element, spectral Galerkin, and discontinuous Galerkin methods. The main idea of the proposed vanishing moment method is to approximate a fully nonlinear second order PDE by a higher order, in particular, a quasilinear fourth order PDE. We show by various numerical experiments the viability of the proposed vanishing moment method. All our numerical experiments show the convergence of the vanishing moment method, and they also show that moment solutions coincide with viscosity solutions whenever the latter exist.
Starting Page	74
Ending Page	98
Page Count	25
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	38
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2008-07-19
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fully nonlinear PDEs Monge-Ampère type equations Moment solutions Vanishing moment method Viscosity solutions Finite element method Mixed finite element method Spectral and discontinuous Galerkin methods Mathematical and Computational Physics ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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