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ANALYSIS OF AN AUGMENTED MIXED-PRIMAL FORMULATION FOR THE STATIONARY BOUSSINESQ PROBLEM

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dc.creatorELIGIO ANTONIO COLMENARES GARCÍA
dc.creatorRICARDO ELVIS OYARZÚA VARGAS
dc.date2016
dc.date.accessioned2025-01-10T14:31:25Z
dc.date.available2025-01-10T14:31:25Z
dc.date.issued2016
dc.description.abstractIN THIS ARTICLE, WE PROPOSE AND ANALYZE A NEW MIXED VARIATIONAL FORMULATION FOR THE STATIONARY BOUSSINESQ PROBLEM. OUR METHOD, WHICH USES A TECHNIQUE PREVIOUSLY APPLIED TO THE NAVIER?STOKES EQUATIONS, IS BASED FIRST ON THE INTRODUCTION OF A MODIFIED PSEUDOSTRESS TENSOR DEPENDING NONLINEARLY ON THE VELOCITY THROUGH THE RESPECTIVE CONVECTIVE TERM. NEXT, THE PRESSURE IS ELIMINATED, AND AN AUGMENTED APPROACH FOR THE FLUID FLOW, WHICH INCORPORATES GALERKIN-TYPE TERMS ARISING FROM THE CONSTITUTIVE AND EQUILIBRIUM EQUATIONS, AND FROM THE DIRICHLET BOUNDARY CONDITION, IS COUPLED WITH A PRIMAL-MIXED SCHEME FOR THE MAIN EQUATION MODELING THE TEMPERATURE. IN THIS WAY, THE ONLY UNKNOWNS OF THE RESULTING FORMULATION ARE GIVEN BY THE AFOREMENTIONED NONLINEAR PSEUDOSTRESS, THE VELOCITY, THE TEMPERATURE, AND THE NORMAL DERIVATIVE OF THE LATTER ON THE BOUNDARY. AN EQUIVALENT FIXED-POINT SETTING IS THEN INTRODUCED AND THE CORRESPONDING CLASSICAL BANACH THEOREM, COMBINED WITH THE LAX?MILGRAM THEOREM AND THE BABU?KA?BREZZI THEORY, ARE APPLIED TO PROVE THE UNIQUE SOLVABILITY OF THE CONTINUOUS PROBLEM. IN TURN, THE BROUWER AND THE BANACH FIXED-POINT THEOREMS ARE USED TO ESTABLISH EXISTENCE AND UNIQUENESS OF SOLUTION, RESPECTIVELY, OF THE ASSOCIATED GALERKIN SCHEME. IN PARTICULAR, RAVIART?THOMAS SPACES OF ORDER K FOR THE PSEUDOSTRESS, CONTINUOUS PIECEWISE POLYNOMIALS OF DEGREE ? K+1 FOR THE VELOCITY AND THE TEMPERATURE, AND PIECEWISE POLYNOMIALS OF DEGREE ? K FOR THE BOUNDARY UNKNOWN BECOME FEASIBLE CHOICES. FINALLY, WE DERIVE OPTIMAL A PRIORI ERROR ESTIMATES, AND PROVIDE SEVERAL NUMERICAL RESULTS ILLUSTRATING THE GOOD PERFORMANCE OF THE AUGMENTED MIXED-PRIMAL FINITE ELEMENT METHOD AND CONFIRMING THE THEORETICAL RATES OF CONVERGENCE.
dc.formatapplication/pdf
dc.identifier.doi10.1002/num.22001
dc.identifier.issn1098-2426
dc.identifier.issn0749-159X
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/7802
dc.languagespa
dc.publisherNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
dc.relation.uri10.1002/num.22001
dc.rightsPUBLICADA
dc.titleANALYSIS OF AN AUGMENTED MIXED-PRIMAL FORMULATION FOR THE STATIONARY BOUSSINESQ PROBLEM
dc.title.alternativeANÁLISIS DE UNA FORMULACIÓN PRIMAL MIXTA AUMENTADA PARA EL PROBLEMA ESTACIONARIO DE BOUSSINESQ
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCHILLÁN
ubb.SedeCONCEPCIÓN
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