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CONVERGENCE OF A LEVEL-SET ALGORITHM IN SCALAR CONSERVATION LAWS

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dc.creatorANÍBAL CORONEL PÉREZ
dc.creatorPATRICIO ANDRÉS CUMSILLE ATALA
dc.date2015
dc.date.accessioned2025-01-10T14:35:23Z
dc.date.available2025-01-10T14:35:23Z
dc.date.issued2015
dc.description.abstractTHIS ARTICLE IS CONCERNED WITH THE CONVERGENCE OF THE LEVEL-SET ALGORITHM INTRODUCED BY ASLAM (J COMPUT PHYS 167 (2001), 413?438) FOR TRACKING THE DISCONTINUITIES IN SCALAR CONSERVATION LAWS IN THE CASE OF LINEAR OR STRICTLY CONVEX FLUX FUNCTION. THE NUMERICAL METHOD IS DEDUCED BY THE LEVEL-SET REPRESENTATION OF THE ENTROPY SOLUTION: THE ZERO OF A LEVEL-SET FUNCTION IS USED AS AN INDICATOR OF THE DISCONTINUITY CURVES AND TWO AUXILIARY STATES, WHICH ARE ASSUMED CONTINUOUS THROUGH THE DISCONTINUITIES, ARE INTRODUCED. WE REWRITE THE NUMERICAL LEVEL-SET ALGORITHM AS A PROCEDURE CONSISTING OF THREE BIG STEPS: (A) INITIALIZATION, (B) EVOLUTION, AND (C) RECONSTRUCTION. IN (A), WE CHOOSE AN ENTROPY ADMISSIBLE LEVEL-SET REPRESENTATION OF THE INITIAL CONDITION. IN (B), FOR EACH ITERATION STEP, WE SOLVE AN UNCOUPLED SYSTEM OF THREE EQUATIONS AND SELECT THE ENTROPY ADMISSIBLE LEVEL-SET REPRESENTATION OF THE SOLUTION PROFILE AT THE END OF THE TIME ITERATION. IN (C), WE RECONSTRUCT THE ENTROPY SOLUTION USING THE LEVEL-SET REPRESENTATION. WE PROVE THE CONVERGENCE OF THE NUMERICAL SOLUTION TO THE ENTROPY SOLUTION IN FOR EVERY , USING -WEAK BOUNDED VARIATION (BV) ESTIMATES AND A CELL ENTROPY INEQUALITY. IN ADDITION, SOME NUMERICAL EXAMPLES FOCUSED ON THE ELEMENTARY WAVE INTERACTION ARE PRESENTED. © 2014 WILEY PERIODICALS, INC. NUMER METHODS PARTIAL DIFFERENTIAL EQ, 2014
dc.formatapplication/pdf
dc.identifier.doi10.1002/num.21953
dc.identifier.issn1098-2426
dc.identifier.issn0749-159X
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/8090
dc.languagespa
dc.publisherNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
dc.relation.uri10.1002/num.21953
dc.rightsPUBLICADA
dc.titleCONVERGENCE OF A LEVEL-SET ALGORITHM IN SCALAR CONSERVATION LAWS
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
ubb.SedeCHILLÁN
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