A Local Discontinuous Galerkin approximation for the $p$-Navier-Stokes system, Part I: Convergence analysis
| Autor: | Kaltenbach, Alex, Růžička, Michael |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the present paper, we propose a Local Discontinuous Galerkin (LDG) approximation for fully non-homogeneous systems of $p$-Navier-Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori estimates), and weak convergence of the method. To this end, we propose a new DG discretization of the convective term and develop an abstract non-conforming theory of pseudo-monotonicity, which is applied to our problem. We also use our approach to treat the $p$-Stokes problem. Comment: 26 pages, 4 tables |
| Databáze: | arXiv |
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