aDepartment of Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100, China
Abstract:
Two Crank–Nicolson least-squares Galerkin finite element schemes are formulated to solve parabolic integro-differential equations. The advantage of this method is that it is not subject to the LBB condition. The convergence analysis shows that the methods yield the approximate solutions with optimal accuracy in H(div; Ω) × H1(Ω) and (L2(Ω))2 × L2(Ω), respectively. Moreover, the two methods both get the approximate solutions with second-order accuracy in time increment.