Incorporating variable viscosity in vorticity-based formulations for Brinkman equations |
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| Authors: | Verónica Anaya Bryan Gómez-Vargas David Mora Ricardo Ruiz-Baier |
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| Institution: | 1. GIMNAP, Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile;3. Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile;4. Sección de Matemática, Sede de Occidente, Universidad de Costa Rica, San Ramón de Alajuela, Costa Rica;5. Mathematical Institute, University of Oxford, A. Wiles Building, Woodstock Road, Oxford OX2 6GG, UK |
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| Abstract: | In this brief note, we introduce a non-symmetric mixed finite element formulation for Brinkman equations written in terms of velocity, vorticity, and pressure with non-constant viscosity. The analysis is performed by the classical Babu?ka–Brezzi theory, and we state that any inf–sup stable finite element pair for Stokes approximating velocity and pressure can be coupled with a generic discrete space of arbitrary order for the vorticity. We establish optimal a priori error estimates, which are further confirmed through computational examples. |
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