A split least-squares characteristic mixed finite element method for Sobolev equations with convection term

In this paper, a split least-squares characteristic mixed finite element method for a kind of Sobolev equation with convection term is proposed, in which the characteristic method is based on the approximation of the material derivative term, that is, the time derivative term plus the convection term. The resulting least-squares procedure can be split into two independent symmetric positive definite sub-schemes and does not need to solve a coupled system of equations. Theory analysis shows that the method yields the approximate solutions with optimal accuracy in L2(Ω) norm for the primal unknown and in H(div;Ω) norm for the unknown flux, respectively. Numerical examples in one dimension, which are consistent with the theoretical results, are provided to demonstrate the characteristic behavior of this approach.