We investigate the effect of the streamline upwind Petrov-Galerkin method (SUPG) as it relates to the moving mesh partial differential equation (MMPDE) method for convection-diffusion problems in the presence of vanishing diffusivity. We first discretize in space using linear finite elements and then use a $\theta$-scheme to discretize in time. On a fixed mesh, SUPG (FM-SUPG) is shown to enhance the stability and resolves spurious oscillations when compared to the classic Galerkin method (FM-FEM) when diffusivity is small. However, it falls short when the layer-gradient is large. In this paper, we develop a moving mesh upwind Petrov-Galerkin (MM-SUPG) method by integrating the SUPG method with the MMPDE method. Numerical results show that our MM-SUPG works well for these types of problems and performs better than FM-SUPG as well as MMPDE without SUPG.

翻译：我们调查了中风Petrov-Galerkin(SUPG)简化方法(SUPG)的影响,因为它与移动网状部分差分方程(MMPDE)方法(MMPDE)有关,因为它在消散时会发生对流扩散问题。我们首先使用线性限量元素在空间中分解,然后使用美元-美元-Scheme来及时分解。在固定网状中,SUPG(F-SUPG)显示,与典型的Galerkin方法(FM-FEM)相比,当 diffusity(FM-FEM)小时,SUPG(F-FEM)可以增强稳定性和解决虚假的振荡。然而,当层位高度大时,它就不够了。在本文中,我们开发了一种移动中风式Petrov-Galkin(M-SUPG)方法,将SPG方法与MPG方法结合。数字结果显示,我们的M-SPG对这些类型的问题非常有效,并且表现优于F-SPG,并且没有MMPDE。