2023/08/28 by Dmitri Kuzmin, Kuzmin, Dmitri, Mária Lukáčová-Medviďová +3 · 2 citations
Engineering · Mathematics · #65M12 65M60 65M70 #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Bounded function #Computational Fluid Dynamics and Aerodynamics #Conservation law #Convergence (economics) #Dissipative system #FOS: Mathematics #Finite element method #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Nonlinear system #Numerical Analysis (math.NA) #Physics #Weak convergence
paper · pdf · doi:10.48550/arxiv.2308.14872
openalex publication_date 2023/08/28 · openalex created_date 2023/08/31 · openalex updated_date 2026/07/28
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a Lax--Wendroff-type theorem for the corresponding semi-discrete problem. A key component of our analysis is the use of a weak estimate on bounded variation, which follows from the semi-discrete entropy stability property of the method under investigation. For the Euler equations of gas dynamics, we prove the weak convergence of the flux-corrected finite element scheme to a dissipative weak solution. If a strong solution exists, the sequence of numerical approximations converges strongly to the strong solution.