Numerical Simulation Of Weak Galerkin Mixd Finite Element Method For Two Kinds Of Evolution Equations

Weak Galerkin(WG)finite element method is a new numerical method which replaces traditional differential operator by weak operator and adds stability item to ensure the continuity of weak solutions.It allows the use of discontinuous functions and has been widely applied to various partial differential equations.In this paper,we mainly study the weak Galerkin mixed finite element method for evolution equa-tions(parabolic equations and parabolic integro-differential equations).we develop the semidiscrete and the fully discrete mixed finite element schemes and proved the existence and uniqueness of the approximation as well as the error estimations of(?)·(?)and L2 norms.There are some differences between the evolution equations we discuss.In the finite element approximation of the parabolic equations,we get the semidiscrete and Crank-Nicolson(C-N)fully discrete weak galerkin mixed finite element schemes and prove the existence and uniqueness of the approximation as well as the error estimations.In the numerical experiments,we solve the parabolic equations under the Robin boundary conditions by using the weak Galerkin mixed finite element approximations with spaces {[Px(T)]2,Pk(e),Pk+1(T)} for k= 0,1,respectively.While studying parabolic integro-differential equations,we get the semidiscrete and backward Euler fully discrete weak galerkin mixed finite elemen-t schemes and prove the existence and uniqueness of the approximation as well as the error estimations.we introduced generalized elliptical projections in addi-tion.And the proofs of uniqueness and approximation properties are given.The final numerical examples analyze the convergence estimates of the lowest order un-der homogeneous Dirichlet boundary and numerical results are given to verify our analysis for the scheme.