  In this paper, we provide a procedure to solve the eigen solutions of Dirac
equation with complicated potential approximately. At first, we solve the eigen
solutions of a linear Dirac equation with complete eigen system, which
approximately equals to the original equation. Take the eigen functions as base
of Hilbert space, and expand the spinor on the bases, we convert the original
problem into solution of extremum of an algebraic function on the unit sphere
of the coefficients. Then the problem can be easily solved. This is a standard
finite element method with strict theory for convergence and effectiveness.
