Anguelov, RoumenLubuma, Jean M.-S.Minani, Froduald2010-07-262010-07-262010-01Anguelov, 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]0170-421410.1002/mma.1148http://hdl.handle.net/2263/14541A 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© 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.Nonstandard finite difference methodMonotone schemeHamilton-Jacobi equations -- Numerical solutionsFinite element methodPreprint Article