A mass-conservative characteristic splitting mixed finite element method for convection-dominated Sobolev equation.

In this article, a new characteristic splitting mixed finite element method is proposed for solving convection-dominated Sobolev equation. In this algorithm the mass-conservative characteristic (MCC) scheme is applied to approximate the time derivative term plus the convection term, and the splitting mixed finite element (SMFE) technique is used to approximate the primal unknown function and the introduced unknown flux. This procedure not only keeps the mass balance but also results in a splitting symmetric positive definite mixed system where we do not need to solve a coupled system. The convergence analysis is considered and the corresponding optimal error estimates in L2 norm for the primal unknown and in H(div) norm for the unknown flux are derived, respectively. Numerical examples are provided to confirm the theoretical results.