The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-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.

翻译：对偶特征-伽辽金方法(DCGM)具有守恒性、精确性和实验上的正定性。本文提出了该方法，并证明了在纽曼边界条件下的收敛性和$L^2$-稳定性。在二维数值有限元框架(FEM)中，将该方法与原始特征-伽辽金方法(PCGM)、流线迎风格式(SUPG)、对偶间断伽辽金方法(DDG)以及无迎风中心有限元方法进行了比较。DCGM在数值实现上较为困难，但在本文的数值背景下，其性能远优于其他所有方法。