Two splitting positive definite mixed finite element methods for parabolic integro-differential equations

Two novel mixed finite element procedures are established for parabolic integro-differential equations, which can be split into two independent symmetric positive definite sub-schemes and do not need to solve a coupled system of equations without requiring the LBB consistency condition. The convergence analysis shows that both methods lead to the optimal order L2(Ω) norm error estimate for u and optimal H(div;Ω) norm error estimate for σ. A numerical example is presented to illustrate the theoretical analysis.