Abstract:

An upwind-mixed method is presented to simulate the linear Sobolev equation in finite element space. The convection term in the linear Sobolev equation is approximated by the upwind method and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Optimal rate error estimates in L²-norm can be obtained. Finally, numerical experiment is given to illustrate the efficiency of the method.

Key words:  upwind-mixed method; linear Sobolev equation; optimal error estimates