A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems
Numerical Analysis
2015-05-25 v1
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.
Cite
@article{arxiv.1505.05984,
title = {A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems},
author = {Masahisa Tabata and Shinya Uchiumi},
journal= {arXiv preprint arXiv:1505.05984},
year = {2015}
}