The Studies Of Galerkin Mixed Element Methods For Two Classes Of Nonlinear Time Fractional Coupled Equations

In this thesis,a Galerkin mixed element algorithm is developed for solving the two-dimensional time fractional coupled sub-diffusion models covering a nonlinear term and two-dimensional coupled Burgers systems with the time fractional derivative.The main research contents are as followsIn Chapter 2,a Galerkin mixed element method combined with the second-order Crank-Nicolson scheme including the WSGD approximation is considered to solve the two-dimensional nonlinear time-fractional coupled sub-diffusion equations.Fully discrete mixed element system including four equations is formulated by introducing two auxiliary variables ?=?u and ?=?v.The existence and uniqueness of the mixed element solution are proven by making use of the matrix theory,the analyses of the stability and a priori error estimates are done,and two numerical examples are shown to confirm the correctness of the theory resultsIn Chapter 3,the mixed element algorithm as considered in Chapter 2,which is combined with the BDF2 approximation with the L1 formula,is simulated for a two-dimensional time fractional coupled Burgers equations.Fully discrete mixed element scheme is constructed and the detailed computing process of the current numerical algo-rithm is provided.Finally,two specific examples are given to verify the effectiveness of the algorithm,and to explore the impact of the convection term and weak singularity of the fractional derivative for the numerical computing.