An Expanded Characteristics-Mixed Finite Element Method for Quasilinear Convection-Dominated Diffusion Equations
拟线性对流占优扩散方程的扩展特征混合有限元方法数值模拟

An expanded characteristics-mixed finite element method for quasilinear convection-dominated diffusion equations is considered, here the characteristic approximation is to handle the convection part in time and the expanded mixed finite element spatial approximation is to deal with the diffusion part. The scheme is stable since fluid is transported along the approximate characteristics on the discrete level. The method expands the standard mixed finite element method in the sense that three variables are optimally and simulataneously treated: the scalar unknown, its gradient and flux. Theoretical analysis and numerical simulation that this method is stable and its $L^{2}$-error estimate is optimal.