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dc.date.accessioned2013-03-12T08:17:03Z
dc.date.available2013-03-12T08:17:03Z
dc.date.issued2004en_US
dc.date.submitted2009-11-30en_US
dc.identifier.urihttp://hdl.handle.net/10852/10627
dc.description.abstractWe 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.isoengen_US
dc.publisherMatematisk Institutt, Universitetet i Oslo
dc.relation.ispartofPreprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076en_US
dc.relation.urihttp://urn.nb.no/URN:NBN:no-8076
dc.titleA CONVERGENCE RATE FOR SEMI-DISCRETE SPLITTING APPROXIMATIONS FOR DEGENERATE PARABOLIC EQUATIONS WITH SOURCE TERMSen_US
dc.typeResearch reporten_US
dc.date.updated2009-11-30en_US
dc.creator.authorJakobsen, Espen R.en_US
dc.creator.authorKarlsen, Kenneth H.en_US
dc.subject.nsiVDP::410en_US
dc.identifier.urnURN:NBN:no-23680en_US
dc.type.documentForskningsrapporten_US
dc.identifier.duo97474en_US
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/10627/1/pm32-04.pdf


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