Convergence rate of the spectral difference method on regular triangular meshes
Numerical Analysis
2024-04-17 v1 Numerical Analysis
Abstract
We consider the spectral difference method based on the p-th order Raviart~-- Thomas space (p=1,2,3) on regular triangular meshes for the scalar transport equation. The solution converges with the order p if the transport velocity is parallel to a family of mesh edges and with the order p+1 otherwise. We prove this fact for p=1 and show it for p=1,2,3 in numerical experiments.
Keywords
Cite
@article{arxiv.2404.10391,
title = {Convergence rate of the spectral difference method on regular triangular meshes},
author = {Pavel Bakhvalov},
journal= {arXiv preprint arXiv:2404.10391},
year = {2024}
}