Two-grid Scheme Of Expanded Mixed Finite Element Method For Semilinear Parabolic Integro-differential Equations

Professor Xu Jinchao first proposed a two grid finite element method for the first time,and applied it to solve asymmetric and indefinite linear elliptic partial differen-tial equations.Then,Professor Xu considered the two grid finite element method for semilinear and nonlinear elliptic partial differential equations.Based on the two grid al-gorithm,experts and scholars combined the two grid method with mixed finite element method,finite volume element method and finite difference method to solve nonlinear parabolic problems.In this thesis,we present a two-grid scheme of expanded mixed finite elemen-t method combined with two second-order time discretization schemes for semilinear parabolic integro-differential equations and provide a detailed convergence analysis.On the coarse grid space,we first use the Crank-Nicolson scheme to solve the original nonlinear problem at the first time step,then we utilize the Leap-Frog scheme at the rest time levels.Next,we make use of the known coarse mesh solution and Taylor expan-sion to infer the solution on the fine mesh space.Finally,a numerical example is given to verify the theoretical results.