New error estimates of Lagrange-Galerkin methods for the advection equation

2023/01/09 by Bermejo, Rodolfo, Carpio, Jaime, Saavedra, Laura
#65M12 #65M25 #65M50 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2301.03438

Abstract

We study in this paper new developments of the Lagrange-Galerkin method for the advection equation. In the first part of the article we present a new improved error estimate of the conventional Lagrange-Galerkin method. In the second part, we introduce a new local projection stabilized Lagrange-Galerkin method, whereas in the third part we introduce and analyze a discontinuity-capturing Lagrange-Galerkin method. Also, attention has been paid to the influence of the quadrature rules on the stability and accuracy of the methods via numerical experiments.

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