A Local Discontinuous Galerkin approximation for the p-Navier-Stokes system, Part I: Convergence analysis

2022/08/08 by Alex Kaltenbach, Kaltenbach, Alex, Michael Růžička +1 · 1 citation
Computer Science · Engineering · Mathematics · #35Q35 #65N12 #65N15 #65N30 #76A05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2208.04106

openalex publication_date 2022/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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