The Dual Characteristic-Galerkin Method
Numerical Analysis
2023-12-18 v1 Numerical Analysis
Analysis of PDEs
Abstract
The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and -stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others.
Cite
@article{arxiv.2312.09751,
title = {The Dual Characteristic-Galerkin Method},
author = {Frederic Hecht and Olivier Pironneau},
journal= {arXiv preprint arXiv:2312.09751},
year = {2023}
}