English

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

Numerical Analysis 2023-01-10 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2301.03438,
  title  = {New error estimates of Lagrange-Galerkin methods for the advection equation},
  author = {Rodolfo Bermejo and Jaime Carpio and Laura Saavedra},
  journal= {arXiv preprint arXiv:2301.03438},
  year   = {2023}
}

Comments

26 pages, 10 figures