dc.date.accessioned 2013-03-12T08:17:03Z dc.date.available 2013-03-12T08:17:03Z dc.date.issued 2004 en_US dc.date.submitted 2009-11-30 en_US dc.identifier.uri http://hdl.handle.net/10852/10627 dc.description.abstract We study a semi-discrete splitting method for computing approximate viscosity solutions of the initial value problem for a class of nonlinear degenerate parabolic equations with source terms. It is fairly standard to prove that the semi-discrete splitting approximations converge to the desired viscosity solution as the splitting step $\Dt$ tends to zero. The purpose of this paper is, however, to consider the more difficult problem of providing a precise estimate of the convergence rate. Using viscosity solution techniques we establish the $L^{\infty}$ convergence rate $\mathcal{O}(\sqrt{\Dt})$ for the approximate solutions, and this estimate is robust with respect to the regularity of the solutions. We also provide an extension of this result to weakly coupled systems of equations, and in the case of more regular solutions we recover the ''classical'' rate $\mathcal{O}(\Dt)$. Finally, we analyze in an example a fully discrete splitting method. eng dc.language.iso eng en_US dc.publisher Matematisk Institutt, Universitetet i Oslo dc.relation.ispartof Preprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076 en_US dc.relation.uri http://urn.nb.no/URN:NBN:no-8076 dc.title A CONVERGENCE RATE FOR SEMI-DISCRETE SPLITTING APPROXIMATIONS FOR DEGENERATE PARABOLIC EQUATIONS WITH SOURCE TERMS en_US dc.type Research report en_US dc.date.updated 2009-11-30 en_US dc.creator.author Jakobsen, Espen R. en_US dc.creator.author Karlsen, Kenneth H. en_US dc.subject.nsi VDP::410 en_US dc.identifier.urn URN:NBN:no-23680 en_US dc.type.document Forskningsrapport en_US dc.identifier.duo 97474 en_US dc.identifier.fulltext Fulltext https://www.duo.uio.no/bitstream/handle/10852/10627/1/pm32-04.pdf
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