Publicación:
ANALYSIS OF WEAK GALERKIN MIXED FINITE ELEMENT METHOD BASED ON THE VELOCITY?PSEUDOSTRESS FORMULATION FOR NAVIER?STOKES EQUATION ON POLYGONAL MESHES

dc.creatorZEINAB GHARIBI
dc.date2024
dc.date.accessioned2025-01-10T15:51:50Z
dc.date.available2025-01-10T15:51:50Z
dc.date.issued2024
dc.description.abstractTHE PRESENT ARTICLE INTRODUCES, MATHEMATICALLY ANALYZES, AND NUMERICALLY VALIDATES A NEW WEAK GALERKIN MIXED FINITE ELEMENT METHOD BASED ON BANACH SPACES FOR THE STATIONARY NAVIER?STOKES EQUATION IN PSEUDOSTRESS?VELOCITY FORMULATION. SPECIFICALLY, A MODIFIED PSEUDOSTRESS TENSOR, WHICH DEPENDS ON THE PRESSURE AS WELL AS THE DIFFUSIVE AND CONVECTIVE TERMS, IS INTRODUCED AS AN AUXILIARY UNKNOWN, AND THE INCOMPRESSIBILITY CONDITION IS THEN USED TO ELIMINATE THE PRESSURE, WHICH IS SUBSEQUENTLY COMPUTED USING A POSTPROCESSING FORMULA. CONSEQUENTLY, TO DISCRETIZE THE RESULTING MIXED FORMULATION, IT IS SUFFICIENT TO PROVIDE A TENSORIAL WEAK GALERKIN SPACE FOR THE PSEUDOSTRESS AND A SPACE OF PIECEWISE POLYNOMIAL VECTORS OF TOTAL DEGREE AT MOST ?K? FOR THE VELOCITY. MOREOVER, THE WEAK GRADIENT/DIVERGENCE OPERATOR IS UTILIZED TO PROPOSE THE WEAK DISCRETE BILINEAR FORMS, WHOSE CONTINUOUS VERSION INVOLVES THE CLASSICAL GRADIENT/DIVERGENCE OPERATORS. THE WELL-POSEDNESS OF THE NUMERICAL SOLUTION IS PROVEN USING A FIXED-POINT APPROACH AND THE DISCRETE VERSIONS OF THE BABU?KA?BREZZI THEORY AND THE BANACH?NE?AS?BABU?KA THEOREM. ADDITIONALLY, AN A PRIORI ERROR ESTIMATE IS DERIVED FOR THE PROPOSED METHOD. FINALLY, SEVERAL NUMERICAL RESULTS ILLUSTRATING THE METHOD?S GOOD PERFORMANCE AND CONFIRMING THE THEORETICAL RATES OF CONVERGENCE ARE PRESENTED.
dc.formatapplication/pdf
dc.identifier.doi10.1007/s10915-024-02651-w
dc.identifier.issn1573-7691
dc.identifier.issn0885-7474
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/14006
dc.languagespa
dc.publisherJOURNAL OF SCIENTIFIC COMPUTING
dc.relation.uri10.1007/s10915-024-02651-w
dc.rightsPUBLICADA
dc.subjectWell-posedness
dc.subjectWeak Galerkin
dc.subjectpseudostress-velocity formulation
dc.subjectNavier-Stokes equation
dc.subjectMixed finite element methods
dc.subjectError analysis
dc.titleANALYSIS OF WEAK GALERKIN MIXED FINITE ELEMENT METHOD BASED ON THE VELOCITY?PSEUDOSTRESS FORMULATION FOR NAVIER?STOKES EQUATION ON POLYGONAL MESHES
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
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