Anisotropic meshes and stabilization parameter design of linear SUPG method for 2D convection-dominated convection-diffusion equations
Anisotropic meshes and stabilization parameter design of linear SUPG method for 2D convection-dominated convection-diffusion equations
复制标题
二维对流主导对流扩散方程线性 SUPG 方法的各向异性网格和稳定化参数设计
DOI：
10.1007/s10915-017-0610-9
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Xiaobo Yin
中科院分区：
文献类型：
--
作者：
Yana Di;Hehu Xie;Xiaobo Yin
针对求解二维对流占优对流扩散方程的线性SUPG方法，提出了一种在生成各向异性网格序列的同时选择适当稳定化参数的数值策略.由于离散误差在适当的范数下可以由插值误差及其在不同范数下的变量之和来限定，我们用包含真解的Hessian矩阵、对流场以及三角形的有向边和面积等几何性质的项来代替它们.在此基础上，利用形状、尺寸和等分布要求导出了相应的度量张量和稳定化参数。数值结果验证了所提出的数值策略的稳定性和有效性。
We propose a numerical strategy to generate a sequence of anisotropic meshes and select appropriate stabilization parameters simultaneously for linear SUPG method solving two dimensional convection-dominated convection–diffusion equations. Since the discretization error in a suitable norm can be bounded by the sum of interpolation error and its variants in different norms, we replace them by some terms which contain the Hessian matrix of the true solution, convective field, and the geometric properties such as directed edges and the area of triangles. Based on this observation, the shape, size and equidistribution requirements are used to derive corresponding metric tensor and stabilization parameters. Numerical results are provided to validate the stability and efficiency of the proposed numerical strategy.