2026-04-14T07:59:48Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3473812026-01-16T09:23:37Zcom_2072_1033col_2072_452950

Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem Codina, Ramon Moreno Martínez, Laura Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental Universitat Politècnica de Catalunya. Doctorat en Anàlisi Estructural Centre Internacional de Mètodes Numèrics en Enginyeria Universitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits Àrees temàtiques de la UPC::Física::Física de fluids Viscoelasticity--Mathematical models Stabilized finite element methods Viscoelastic fluids Oldroyd-B Logarithm reformulation High Weissenberg number problem Viscoelasticitat -- Models matemàtics In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper. R. Codina gratefully acknowledges the support received from the ICREA Acad`emia Program, from the Catalan Government. L. Moreno acknowledges the support received from the Spanish Government through a predoctoral FPI Grant. Peer Reviewed Postprint (published version) 2021-02 Article Codina, R.; Moreno, L. Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem. "ESAIM. Mathematical modeling and numerical analysis. Modelisation mathématique", Febrer 2021, vol. 55, núm. S1, p. S279-S300. 0764-583X https://hdl.handle.net/2117/347381 10.1051/m2an/2020038 eng https://www.esaim-m2an.org/articles/m2an/abs/2021/01/m2an200037/m2an200037.html Open Access application/pdf