A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method

dc.contributor.authorAnguelov, Roumen
dc.contributor.authorLubuma, Jean M.-S.
dc.contributor.authorMinani, Froduald
dc.contributor.emailroumen.anguelov@up.ac.zaen_US
dc.date.accessioned2010-07-26T06:36:01Z
dc.date.available2010-07-26T06:36:01Z
dc.date.issued2010-01
dc.description.abstractA usual way of approximating Hamilton-Jacobi equations is to couple space finite element discretization with time finite difference discretization. This classical approach leads to a severe restriction on the time step size for the scheme to be monotone. In this paper, we couple the finite element method with the nonstandard finite difference method, which is based on the Mickens' rule of nonlocal approximation. The scheme obtained in this way is unconditionally monotone. The convergence of the new method is discussed and numerical results that support the theory are provided.en
dc.identifier.citationAnguelov, R, Lubuma, JMS & Minani, F 2010, 'A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method', Mathematical Methods in the Applied Sciences, vol. 33, no. 1, pp. 41-48. [www.interscience.wiley.com]en
dc.identifier.issn0170-4214
dc.identifier.other10.1002/mma.1148
dc.identifier.urihttp://hdl.handle.net/2263/14541
dc.language.isoenen_US
dc.publisherWiley-Blackwellen_US
dc.rights© 2009 John Wiley & Sons, Ltd. This is the pre-peer reviewed version of the following article: Anguelov, R, Lubuma, JMS & Minani, F 2009, 'A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method', Mathematical Methods in the Applied Sciences, vol. 33, no. 1, pp. 1-14 which has been published in final form at www.interscience.wiley.com.en_US
dc.subjectNonstandard finite difference methoden
dc.subjectMonotone schemeen
dc.subject.lcshHamilton-Jacobi equations -- Numerical solutionsen
dc.subject.lcshFinite element methoden
dc.titleA monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference methoden
dc.typePreprint Articleen

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