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2016

An Efficient Filtered Scheme for Some First Order Time-Dependent Hamilton-Jacobi Equations

3 years 6 months ago
An Efficient Filtered Scheme for Some First Order Time-Dependent Hamilton-Jacobi Equations
We introduce a new class of “filtered” schemes for some first order non-linear Hamilton-Jacobi equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013) and Oberman and Salvador (J. Comput. Phys., Vol 284, pp. 367-388, 2015) for steady equations. Here we mainly study the time-dependent setting and focus on fully explicit schemes. Furthermore, specific corrections to the filtering idea are also needed in order to obtain high-order efficiency. The proposed schemes are not monotone but still satisfy some -monotone property. A general convergence result together with a precise error estimate of order √ ∆x are given (∆x is the mesh size). The framework allows to construct finite difference discretizations that are easy to implement and high–order in the domain where the solution is smooth. A novel error estimate is also given in the case of the approximation of steady equations. Numerical tests including evolutive conve...
Olivier Bokanowski, Maurizio Falcone, Smita Sahu
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SIAMSC
Authors Olivier Bokanowski, Maurizio Falcone, Smita Sahu
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