Publicación:
A POSTERIORI ERROR ANALYSIS OF A MOMENTUM AND THERMAL ENERGY CONSERVATIVE MIXED FEM FOR THE BOUSSINESQ EQUATIONS

dc.creatorRICARDO ELVIS OYARZÚA VARGAS
dc.date2022
dc.date.accessioned2025-01-10T15:33:12Z
dc.date.available2025-01-10T15:33:12Z
dc.date.issued2022
dc.description.abstractIN THIS PAPER WE COMPLEMENT THE STUDY OF A NEW MIXED FNITE ELEMENT SCHEME, ALLOWING CONSERVATION OF MOMENTUM AND THERMAL ENERGY, FOR THE BOUSSINESQ MODEL DESCRIBING NATURAL CONVECTION AND DERIVE A RELIABLE AND EFCIENT RESIDUAL-BASED A POSTERIORI ERROR ESTIMATOR FOR THE CORRESPONDING GALERKIN SCHEME IN TWO AND THREE DIMENSIONS. MORE PRECISELY, BY EXTENDING STANDARD TECHNIQUES COMMONLY USED ON HILBERT SPACES TO THE CASE OF BANACH SPACES, SUCH AS LOCAL ESTIMATES, SUITABLE HELMHOLTZ DECOMPOSITIONS AND THE LOCAL APPROXIMATION PROPERTIES OF THE CLÉMENT AND RAVIART?THOMAS OPERATORS, WE DERIVE THE AFOREMENTIONED A POSTERIORI ERROR ESTIMATOR ON ARBITRARY (CONVEX OR NON-CONVEX) POLYGONAL AND POLYHEDRAL REGIONS. IN TURN, INVERSE INEQUALITIES, THE LOCALIZATION TECHNIQUE BASED ON BUBBLE FUNCTIONS, AND KNOWN RESULTS FROM PREVIOUS WORKS, ARE EMPLOYED TO PROVE THE LOCAL EFCIENCY OF THE PROPOSED A POSTERIORI ERROR ESTIMATOR. FINALLY, TO ILLUSTRATE THE PERFORMANCE OF THE ADAPTIVE ALGORITHM BASED ON THE PROPOSED A POSTERIORI ERROR INDICATOR AND TO CORROBORATE THE THEORETICAL RESULTS, WE PROVIDE SOME NUMERICAL EXAMPLES.
dc.formatapplication/pdf
dc.identifier.doi10.1007/s10092-022-00488-z
dc.identifier.issn1126-5434
dc.identifier.issn0008-0624
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/12557
dc.languagespa
dc.publisherCALCOLO
dc.relation.uri10.1007/s10092-022-00488-z
dc.rightsPUBLICADA
dc.subjectSTATIONARY BOUSSINESQ EQUATIONS
dc.subjectRELIABILITY
dc.subjectRAVIART?THOMAS ELEMENTS
dc.subjectMIXED FNITE ELEMENT METHOD
dc.subjectLOCAL EFCIENCY
dc.subjectCONSERVATION OF THERMAL ENERGY
dc.subjectCONSERVATION OF MOMENTUM
dc.subjectBANACH SPACES
dc.subjectA POSTERIORI ERROR ESTIMATOR
dc.titleA POSTERIORI ERROR ANALYSIS OF A MOMENTUM AND THERMAL ENERGY CONSERVATIVE MIXED FEM FOR THE BOUSSINESQ EQUATIONS
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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