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A FULLY-MIXED FINITE ELEMENT METHOD FOR THE STEADY STATE OBERBECK-BOUSSINESQ SYSTEM

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dc.creatorELIGIO ANTONIO COLMENARES GARCÍA
dc.date2020
dc.date.accessioned2025-01-10T15:10:19Z
dc.date.available2025-01-10T15:10:19Z
dc.date.issued2020
dc.description.abstractWE PROPOSE A NEW FULLY-MIXED FORMULATION FOR THE STATIONARY OBERBECK-BOUSSINESQ PROBLEM WHEN VISCOSITY DEPENDS ON BOTH TEMPERATURE AND CONCENTRATION. FOLLOWING SIMILAR IDEAS APPLIED PRE- VIOUSLY TO THE BOUSSINESQ AND NAVIER-STOKES EQUATIONS, WE INCORPORATE THE VELOCITY GRADIENT AND THE BERNOULLI STRESS TENSOR AS AUXILIARY UNKNOWNS OF THE FLUID EQUATIONS. IN TURN, THE GRADIENTS OF TEMPERATURE AND OF CONCENTRATION, IN ADDITION TO A BERNOULLI VECTOR, ARE INTRODUCED AS FURTHER VARIABLES OF THE HEAT AND MASS TRANSFER EQUATIONS. CONSEQUENTLY, A DUAL-MIXED APPROACH WITH DIRICHLET DATA IS DEFINED IN EACH SUB-SYSTEM, AND THE WELL-KNOWN BANACH AND BROUWER THEOREMS ARE COMBINED WITH BABU?SKA-BREZZI?S THEORY IN EACH INDEPENDENT SET OF EQUATIONS, YIELDING THE SOLV- ABILITY OF THE CONTINUOUS AND DISCRETE SCHEMES. NEXT, WE DESCRIBE SPECIFIC FINITE ELEMENT SUBSPACES SATISFYING APPROPRIATE STABILITY REQUIREMENTS, AND DERIVE OPTIMAL A PRIORI ERROR ESTIMATES. FINALLY, SEVERAL NUMERICAL EXAMPLES ILLUSTRATING THE PERFORMANCE OF THE FULLY-MIXED SCHEME AND CONFIRMING THE THEORETICAL RATES OF CONVERGENCE ARE PRESENTED.
dc.formatapplication/pdf
dc.identifier.doi10.5802/smai-jcm.64
dc.identifier.issn2426-8399
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10760
dc.languagespa
dc.publisherSMAI JOURNAL OF COMPUTATIONAL MATHEMATICS
dc.relation.uri10.5802/smai-jcm.64
dc.rightsPUBLICADA
dc.subjectOberbeck?Boussinesq equations
dc.subjectfully?mixed formulation
dc.subjectfixed-point theory
dc.subjectfinite element methods
dc.subjecta priori error analysis
dc.titleA FULLY-MIXED FINITE ELEMENT METHOD FOR THE STEADY STATE OBERBECK-BOUSSINESQ SYSTEM
dc.title.alternativeUN MÉTODO DE ELEMENTOS FINITOS COMPLETAMENTE MEZCLADO PARA EL SISTEMA DE ESTADO ESTACIONARIO DE OBERBECK-BOUSSINESQ
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
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