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AN AUGMENTED VELOCITY-VORTICITY-PRESSURE FORMULATION FOR THE BRINKMAN EQUATIONS

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dc.creatorVERÓNICA JULIA ANAYA DOMÍNGUEZ
dc.creatorDAVID ANDRÉS MORA HERRERA
dc.date2015
dc.date.accessioned2025-01-10T14:30:58Z
dc.date.available2025-01-10T14:30:58Z
dc.date.issued2015
dc.description.abstractTHIS PAPER DEALS WITH THE ANALYSIS OF A NEW AUGMENTED MIXED FINITE ELEMENT METHOD IN TERMS OF VORTICITY, VELOCITY, AND PRESSURE, FOR THE BRINKMAN PROBLEM WITH NONSTANDARD BOUNDARY CONDITIONS. THE APPROACH IS BASED ON THE INTRODUCTION OF GALERKIN LEAST-SQUARES TERMS ARISING FROM THE CONSTITUTIVE EQUATION RELATING THE AFOREMENTIONED UNKNOWNS AND FROM THE INCOMPRESSIBILITY CONDITION. WE SHOW THAT THE RESULTING AUGMENTED BILINEAR FORM IS CONTINUOUS AND ELLIPTIC, WHICH, THANKS TO THE LAX?MILGRAM THEOREM, AND BESIDES PROVING THE WELL-POSEDNESS OF THE CONTINUOUS FORMULATION, ENSURES THE SOLVABILITY AND STABILITY OF THE GALERKIN SCHEME WITH ANY FINITE ELEMENT SUBSPACE OF THE CONTINUOUS SPACE. IN PARTICULAR, RAVIART?THOMAS ELEMENTS OF ANY ORDER URN:X-WILEY:FLD:MEDIA:FLD4041:FLD4041-MATH-0001 FOR THE VELOCITY FIELD, AND PIECEWISE CONTINUOUS POLYNOMIALS OF DEGREE K + 1 FOR BOTH THE VORTICITY AND THE PRESSURE, CAN BE UTILIZED. A PRIORI ERROR ESTIMATES AND THE CORRESPONDING RATES OF CONVERGENCE ARE ALSO GIVEN HERE. NEXT, WE DERIVE TWO RELIABLE AND EFFICIENT RESIDUAL-BASED A POSTERIORI ERROR ESTIMATORS FOR THIS PROBLEM. THE ELLIPTICITY OF THE BILINEAR FORM TOGETHER WITH THE LOCAL APPROXIMATION PROPERTIES OF THE CLÉMENT INTERPOLATION OPERATOR ARE THE MAIN TOOLS FOR SHOWING THE RELIABILITY. IN TURN, INVERSE INEQUALITIES AND THE LOCALIZATION TECHNIQUE BASED ON TRIANGLE-BUBBLE AND EDGE-BUBBLE FUNCTIONS ARE UTILIZED TO SHOW THE EFFICIENCY. FINALLY, SEVERAL NUMERICAL RESULTS ILLUSTRATING THE GOOD PERFORMANCE OF THE METHOD, CONFIRMING THE PROPERTIES OF THE ESTIMATORS AND SHOWING THE BEHAVIOR OF THE ASSOCIATED ADAPTIVE ALGORITHMS, ARE REPORTED. COPYRIGHT © 2015 JOHN WILEY & SONS, LTD.
dc.formatapplication/pdf
dc.identifier.doiorg/10.1002/fld.4041
dc.identifier.issn1097-0363
dc.identifier.issn0271-2091
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/7770
dc.languagespa
dc.publisherINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
dc.relation.uriorg/10.1002/fld.4041
dc.rightsPUBLICADA
dc.titleAN AUGMENTED VELOCITY-VORTICITY-PRESSURE FORMULATION FOR THE BRINKMAN EQUATIONS
dc.title.alternativeUNA FORMULACIÓN DE VELOCIDAD-VORTICIDAD-PRESIÓN AUMENTADA PARA LAS ECUACIONES DE BRINKMAN
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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