论文标题
分析具有1D非线性对流扩散系统的广义通量的局部不连续的盖尔金方法
Analysis of the local discontinuous Galerkin method with generalized fluxes for 1D nonlinear convection-diffusion systems
论文作者
论文摘要
在本文中，我们介绍了一维非线性对流 - 扩散系统的局部不连续的Galerkin方法的最佳误差估计。基于局部特征分解，选择了对流术语具有可调节数值粘度的前风偏置通量，这有助于解决不限制程序的不限制抛物线方程的不连续性。对于扩散术语，考虑了一对广义交替通量。通过在不同的对流或扩散术语方面构建和分析广义的高斯 - 拉达预测，我们通过具有同样的可对称性通量Jacobian和完全非线性扩散问题的非线性对流对流扩散系统得出了最佳的误差估计。提供了数值实验，包括长时间模拟，不同的边界条件和具有不连续初始数据的退化方程，以证明理论结果的清晰度。
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear convection-diffusion systems. The upwind-biased flux with adjustable numerical viscosity for the convective term is chosen based on the local characteristic decomposition, which is helpful in resolving discontinuities of degenerate parabolic equations without enforcing any limiting procedure. For the diffusive term, a pair of generalized alternating fluxes are considered. By constructing and analyzing generalized Gauss-Radau projections with respect to different convective or diffusive terms, we derive optimal error estimates for nonlinear convection-diffusion systems with the symmetrizable flux Jacobian and fully nonlinear diffusive problems. Numerical experiments including long time simulations, different boundary conditions and degenerate equations with discontinuous initial data are provided to demonstrate the sharpness of theoretical results.
