In this talk, I shall present some local multilevel algorithms for solving the linear algebraic systems arising from the adaptive discontinuous finite element methods. The abstract Schwarz theory is applied to analyze the multilevel methods with Jacobi or Gauss-Seidel smoother performed on local nodes on each level. It is shown that the local multilevel methods are optimal, which means that the convergence rates are independent of the mesh sizes and mesh levels. Numerical results shall be given to confirm our theoretical findings.