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A BANACH SPACES-BASED FULLY-MIXED FINITE ELEMENT METHOD FOR THE STATIONARY CHEMOTAXIS-NAVIER-STOKES PROBLEM

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dc.creatorELIGIO ANTONIO COLMENARES GARCÍA
dc.date2023
dc.date.accessioned2025-01-10T15:39:49Z
dc.date.available2025-01-10T15:39:49Z
dc.date.issued2023
dc.description.abstractIN THIS PAPER WE INTRODUCE AND ANALYZE A BANACH SPACES-BASED APPROACH YIELDING A FULLY-MIXED FINITE ELEMENT METHOD FOR NUMERICALLY SOLVING THE STATIONARY CHEMOTAXIS-NAVIER-STOKES PROBLEM. THIS IS A NONLINEAR COUPLED MODEL REPRESENTING THE BIOLOGICAL PROCESS GIVEN BY THE CELL MOVEMENT, DRIVEN BY EITHER AN INTERNAL OR AN EXTERNAL CHEMICAL SIGNAL, WITHIN AN INCOMPRESSIBLE FLUID. IN ADDITION TO THE VELOCITY AND PRESSURE OF THE FLUID, THE VELOCITY GRADIENT AND THE BERNOUILLI-TYPE STRESS TENSOR ARE INTRODUCED AS FURTHER UNKNOWNS, WHICH ALLOWS TO ELIMINATE THE PRESSURE FROM THE EQUATIONS AND COMPUTE IT AFTERWARDS VIA A POSTPROCESSING FORMULA. IN TURN, BESIDES THE CELL DENSITY AND THE CHEMICAL SIGNAL CONCENTRATION, THE PSEUDOSTRESS ASSOCIATED WITH THE FORMER AND THE GRADIENT OF THE LATTER ARE INTRODUCED AS AUXILIARY UNKNOWNS AS WELL. THE RESULTING CONTINUOUS FORMULATION, POSED IN SUITABLE BANACH SPACES, CONSISTS OF A COUPLED SYSTEM OF THREE SADDLE POINT-TYPE PROBLEMS, EACH ONE OF THEM PERTURBED WITH TRILINEAR FORMS THAT DEPEND ON DATA AND THE UNKNOWNS OF THE OTHER TWO. THE WELL-POSEDNESS OF IT IS ANALYZED BY MEANS OF A FIXED-POINT STRATEGY, SO THAT THE CLASSICAL BANACH THEOREM, ALONG WITH THE BABUSKA-BREZZI THEORY IN BANACH SPACES, ALLOW TO CONCLUDE, UNDER A SMALLNESS ASSUMPTION ON THE DATA, THE EXISTENCE OF A UNIQUE SOLUTION. ADOPTING AN ANALOGUE APPROACH FOR THE ASSOCIATED GALERKIN SCHEME, AND UNDER SUITABLE HYPOTHESES ON ARBITRARY FINITE ELEMENT SUBSPACES EMPLOYED, WE APPLY THE BROUWER AND BANACH THEOREMS TO SHOW EXISTENCE AND THEN UNIQUENESS OF THE DISCRETE SOLUTION. GENERAL A PRIORI ERROR ESTIMATES, INCLUDING THOSE FOR THE POSTPROCESSED PRESSURE, ARE ALSO DERIVED.
dc.formatapplication/pdf
dc.identifier.doi10.1016/j.camwa.2023.06.006
dc.identifier.issn1873-7668
dc.identifier.issn0898-1221
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/13077
dc.languagespa
dc.publisherCOMPUTERS & MATHEMATICS WITH APPLICATIONS
dc.relation.uri10.1016/j.camwa.2023.06.006
dc.rightsRESTRICTED ACCESS
dc.subjectBabuska-Brezzi
dc.subjectNavier-Stokes
dc.subjectMixed finite element methods
dc.subjectFixed-point
dc.subjectChemotaxis
dc.subjectBanach framework
dc.titleA BANACH SPACES-BASED FULLY-MIXED FINITE ELEMENT METHOD FOR THE STATIONARY CHEMOTAXIS-NAVIER-STOKES PROBLEM
dc.typeARTÍCULO
dspace.entity.typePublication
oaire.fundingReferenceANID- AGENCIA NACIONAL DE INVESTIGACIÓN Y DESARROLLO (EX CONICYT)
oaire.fundingReferenceANID- AGENCIA NACIONAL DE INVESTIGACIÓN Y DESARROLLO (EX CONICYT)
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.SedeCHILLÁN
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