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A POSTERIORI ERROR ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR THE COUPLED BRINKMAN-FORCHHEIMER AND DOUBLE-DIFFUSION EQUATIONS

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dc.creatorRICARDO ELVIS OYARZÚA VARGAS
dc.date2022
dc.date.accessioned2025-01-10T15:33:13Z
dc.date.available2025-01-10T15:33:13Z
dc.date.issued2022
dc.description.abstractIN THIS PAPER WE CONSIDER A PARTIALLY AUGMENTED FULLY-MIXED VARIATIONAL FORMULATION THAT HAS BEEN RECENTLY PROPOSED FOR THE COUPLING OF THE STATIONARY BRINKMAN?FORCHHEIMER AND DOUBLE DIFFUSION EQUATIONS, AND DEVELOP AN A POSTERIORI ERROR ANALYSIS FOR THE 2D AND 3D VERSIONS OF THE ASSOCIATED MIXED FINITE ELEMENT SCHEME. INDEED, WE DERIVE TWO RELIABLE AND EFFICIENT RESIDUAL-BASED A POSTERIORI ERROR ESTIMATORS FOR THIS PROBLEM ON ARBITRARY (CONVEX OR NONCONVEX) POLYGONAL AND POLYHEDRAL REGIONS. THE RELIABILITY OF THE PROPOSED ESTIMATORS DRAWS MAINLY UPON THE UNIFORM ELLIPTICITY AND INF-SUP CONDITION OF THE FORMS INVOLVED, A SUITABLE ASSUMPTION ON THE DATA, STABLE HELMHOLTZ DECOMPOSITIONS IN HILBERT AND BANACH FRAMEWORKS, AND THE LOCAL APPROXIMATION PROPERTIES OF THE CLÉMENT AND RAVIART?THOMAS OPERATORS. IN TURN, INVERSE INEQUALITIES, THE LOCALIZATION TECHNIQUE BASED ON BUBBLE FUNCTIONS, AND KNOWN RESULTS FROM PREVIOUS WORKS, ARE THE MAIN TOOLS YIELDING THE EFFICIENCY ESTIMATE. FINALLY, SEVERAL NUMERICAL EXAMPLES CONFIRMING THE THEORETICAL PROPERTIES OF THE ESTIMATORS AND ILLUSTRATING THE PERFORMANCE OF THE ASSOCIATED ADAPTIVE ALGORITHMS, ARE REPORTED. IN PARTICULAR, THE CASEOF FLOW THROUGH A 3D POROUS MEDIA WITH CHANNEL NETWORKS IS CONSIDERED.
dc.formatapplication/pdf
dc.identifier.doi10.1007/s10915-022-02010-7
dc.identifier.issn1573-7691
dc.identifier.issn0885-7474
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/12558
dc.languagespa
dc.publisherJOURNAL OF SCIENTIFIC COMPUTING
dc.relation.uri10.1007/s10915-022-02010-7
dc.rightsPUBLICADA
dc.subjectSTRESS-VELOCITY FORMULATION
dc.subjectMIXED FINITE ELEMENT METHODS
dc.subjectDOUBLE-DIFFUSION EQUATIONS
dc.subjectBRINKMAN?FORCHHEIMER EQUATIONS
dc.subjectA POSTERIORI ERROR ANALYSIS
dc.titleA POSTERIORI ERROR ANALYSIS OF A MIXED FINITE ELEMENT METHOD FOR THE COUPLED BRINKMAN-FORCHHEIMER AND DOUBLE-DIFFUSION EQUATIONS
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE MATEMATICA
ubb.SedeCONCEPCIÓN
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