Mixed finite element method for quasilinear degenerate elliptic equations.

The Dirichlet problem for the quasilinear elliptic equations of the second order that admits nonlinear degeneration is considered. A mixed scheme of the finite element method is proposed. The convergence of the discrete mixed problem solution to the generalized solution is investigated. In particular, the strong convergence of discrete flux is established. The iterative methods of the numerical solution of the mixed finite element method schemes are proposed and investigated. There is an example of the application of the proposed numerical methods to the nonlinear seepage theory problem.