English

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 L2L^2-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.

Keywords

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}
}
R2 v1 2026-06-28T13:52:18.474Z