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dc.contributor.authorCagnetti, Filippo
dc.contributor.authorGomes, Diogo A.
dc.contributor.authorTran, Hung Vinh
dc.date.accessioned2015-08-03T11:34:54Z
dc.date.available2015-08-03T11:34:54Z
dc.date.issued2013-11
dc.identifier.citationCagnetti, F., Gomes, D., & Tran, H. V. (2013). Convergence of a semi-discretization scheme for the Hamilton–Jacobi equation: A new approach with the adjoint method. Applied Numerical Mathematics, 73, 2–15. doi:10.1016/j.apnum.2013.05.004
dc.identifier.issn01689274
dc.identifier.doi10.1016/j.apnum.2013.05.004
dc.identifier.urihttp://hdl.handle.net/10754/563062
dc.description.abstractWe consider a numerical scheme for the one dimensional time dependent Hamilton-Jacobi equation in the periodic setting. This scheme consists in a semi-discretization using monotone approximations of the Hamiltonian in the spacial variable. From classical viscosity solution theory, these schemes are known to converge. In this paper we present a new approach to the study of the rate of convergence of the approximations based on the nonlinear adjoint method recently introduced by L.C. Evans. We estimate the rate of convergence for convex Hamiltonians and recover the O(h) convergence rate in terms of the L∞ norm and O(h) in terms of the L1 norm, where h is the size of the spacial grid. We discuss also possible generalizations to higher dimensional problems and present several other additional estimates. The special case of quadratic Hamiltonians is considered in detail in the end of the paper. © 2013 IMACS.
dc.description.sponsorshipF. Cagnetti was supported by the UTAustin vertical bar Portugal partnership through the FCT post-doctoral fellowship SFRH/BPD/51349/2011, CAMGSD-LARSys through FCT Program POCTI-FEDER and by grants PTDC/MAT/114397/2009, UTAustin/MAT/0057/2008, and UTA-CMU/MAT/0007/2009. D. Gomes was partially supported by CAMGSD-LARSys through FCT Program POCTI-FEDER and by grants PTDC/MAT/114397/2009, UTAustin/MAT/0057/2008, and UTA-CMU/MAT/0007/2009. H. Tran was supported in part by VEF fellowship.
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/abs/arXiv:1106.0444v2
dc.subjectAdjoint method
dc.subjectHamilton-Jacobi equation
dc.subjectNumerical scheme
dc.titleConvergence of a semi-discretization scheme for the Hamilton-Jacobi equation: A new approach with the adjoint method
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalApplied Numerical Mathematics
dc.contributor.institutionDepartamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
dc.contributor.institutionDepartment of Mathematics, University of California, Berkeley, CA 94720-3840, United States
dc.identifier.arxivid1106.0444
kaust.personGomes, Diogo A.
dc.date.posted2011-06-02


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