A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems

2015/05/22 by Masahisa Tabata, Tabata, Masahisa, Shinya Uchiumi +1
Engineering · Mathematics · #65M12 #65M25 #65M60 #76M10 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1505.05984

openalex publication_date 2015/05/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We present a Lagrange-Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange-Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. We prove the stability and convergence of the best possible order. Numerical results reflect these estimates.

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