Analysis and Approximation of a Vorticity–Velocity–Pressure Formulation for the Oseen Equations
| Autor: | Nour Seloula, Verónica Anaya, Ricardo Ruiz-Baier, David Mora, Carlos Reales, Héctor Torres, Afaf Bouharguane |
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| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
010103 numerical & computational mathematics
01 natural sciences Theoretical Computer Science Bernoulli's principle Discontinuous Galerkin method Convergence (routing) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics [MATH]Mathematics [math] ComputingMilieux_MISCELLANEOUS Mathematics Numerical Analysis Applied Mathematics General Engineering Numerical Analysis (math.NA) Mixed finite element method Vorticity Finite element method 010101 applied mathematics Computational Mathematics Computational Theory and Mathematics Dynamic pressure Software Oseen equations [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Journal of Scientific Computing Journal of Scientific Computing, Springer Verlag, 2019, 80 (3), pp.1577-1606. ⟨10.1007/s10915-019-00990-7⟩ |
| ISSN: | 0885-7474 1573-7691 |
| DOI: | 10.1007/s10915-019-00990-7⟩ |
| Popis: | We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous problem is addressed by invoking a global inf-sup property in an adequate abstract setting for non-symmetric systems. The proposed finite element schemes, which produce exactly divergence-free discrete velocities, are shown to be well-defined and optimal convergence rates are derived in suitable norms. This mixed finite element method is also pressure-robust. In addition, we establish optimal rates of convergence for a class of discontinuous Galerkin schemes, which employ stabilisation. A set of numerical examples serves to illustrate salient features of these methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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