Superconvergence Analysis Of Finite Element Method For Time-mixed Fractional Diffusion-wave Equation

Fractional partial differential equations are becoming more and more widely used in various fields,and time fractional partial differential equations are a very important type of mathematical model.With the continuous deepening of the study of time fractional partial differential equations,there is less research results on the numerical solutions of a class of time mixed fractional diffusion wave equations[1].This paper combines the finite element method,the higher-order finite difference format and the L1-CN format to construct a fully discrete format,and analyzes the stability of the discrete format.Then,strictly prove the convergence result in the sense of L2 norm and the super approximation result in the sense of H1 norm O(h2+?min{3-?,3-?})(0<?<1,1<?<2)Finally,the operator is interpolated and the overall superconvergence result is derived.The fully discrete approximation scheme given in this paper further improves the integer Body accuracy.The final numerical experiment also verified the theoretical analysis.