Crank-Nicolson split least-squares procedure for nonlocal reactive flow in porous media

In this paper, we introduce a Crank-Nicolson split least-squares Galerkin finite element procedure for parabolic integro-differential equations, arising in the modeling of nonlocal reactive flows in porous media. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. By carefully choosing projections, we get optimal order H ¹(Ω) and L ²(Ω) norm error estimates for u and sub-optimal (L ²(Ω)) ^d norm error estimate for σ with second-order accuracy in time increment. The numerical examples are given to testify the efficiency of the introduced scheme.