A ROBUST DPG METHOD FOR SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS

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dc.contributor.authorHeuer, Norbert
dc.contributor.authorKarkulik, Michael
dc.date.accessioned2025-01-23T21:23:40Z
dc.date.available2025-01-23T21:23:40Z
dc.date.issued2017
dc.description.abstractWe present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start with an ultraweak formulation that comprises parameters alpha, beta to allow for general epsilon-dependent weightings of three field variables (epsilon being the small diffusion parameter). Specific values of alpha and beta imply robustness of the method, that is, a quasi-optimal error estimate with a constant that is independent of epsilon. Moreover, these values lead to a norm for the field variables that is known to be balanced in epsilon for model problems with typical boundary layers. Several numerical examples underline our theoretical estimates and reveal stability of approximations even for very small epsilon.
dc.fuente.origenWOS
dc.identifier.doi10.1137/15M1041304
dc.identifier.eissn1095-7170
dc.identifier.issn0036-1429
dc.identifier.urihttps://doi.org/10.1137/15M1041304
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/101289
dc.identifier.wosidWOS:000404765500005
dc.issue.numero3
dc.language.isoen
dc.pagina.final1242
dc.pagina.inicio1218
dc.revistaSiam journal on numerical analysis
dc.rightsacceso restringido
dc.subjectreaction-dominated diffusion
dc.subjectsingularly perturbed problem
dc.subjectboundary layers
dc.subjectdiscontinuous Petrov-Galerkin method
dc.titleA ROBUST DPG METHOD FOR SINGULARLY PERTURBED REACTION-DIFFUSION PROBLEMS
dc.typeartículo
dc.volumen55
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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