一维非线性对流扩散方程特征有限元的两重网格算法

针对一维非线性对流扩散方程，构造了特征有限元两重网格算法。该算法只需要在粗网格上进行非线性迭代运算，而在所需要求解的细网格上进行一次线性运算即可。对于非线性对流占优扩散方程，不仅可以消除因对流占优项引起的数值振荡现象，更重要的是可以加快收敛速度、提高计算效率。误差估计表明，只要选取粗网格步长与细网格步长的平方根同阶，就可以使两重网格解与有限元解保持同样的计算精度。

Two-Grid Algorithm for Characteristics Finite-Element Solution of 1D Nonlinear Convection-Dominated Diffusion Equation

For one dimensional nonlinear convection diffusion equation, a two-grid method of characteristic finite-element solution is constructed, where the nonlinear iteration is only executed on the coarse grid, then the fine-grid solution can be obtained via a single linear step. For the nonlinear convection-dominated diffusion equation, the method can stabilize the numerical oscillation, accelerate the convergence and improve the computational efficiency. The error analysis demonstrates that if the mesh size of coarse-grid equal to the square root of fine-grid, the two-grid solution of the characteristic finite-element and the iteration solution of characteristic finite-element have the same order of accuracy.