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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2016

12-05-2016

An Accelerated Method for Nonlinear Elliptic PDE

Authors: Hayden Schaeffer, Thomas Y. Hou

Published in: Journal of Scientific Computing | Issue 2/2016

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Abstract

We propose two numerical methods for accelerating the convergence of the standard fixed point method associated with a nonlinear and/or degenerate elliptic partial differential equation. The first method is linearly stable, while the second is provably convergent in the viscosity solution sense. In practice, the methods converge at a nearly linear complexity in terms of the number of iterations required for convergence. The methods are easy to implement and do not require the construction or approximation of the Jacobian. Numerical examples are shown for Bellman’s equation, Isaacs’ equation, Pucci’s equations, the Monge–Ampère equation, a variant of the infinity Laplacian, and a system of nonlinear equations.
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Appendix
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Metadata
Title
An Accelerated Method for Nonlinear Elliptic PDE
Authors
Hayden Schaeffer
Thomas Y. Hou
Publication date
12-05-2016
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0215-8

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