Convergence Analysis of the Schwarz Algorithm and Multilevel Decomposition Iterative Methods II: Nonselfadjoint and Indefinite Elliptic Problems

Convergence estimate for the Schwarz alternating algorithm applied to nonselfadjoint and indefinite elliptic problems is established for a certain overlapping domain decomposition. Multilevel iterative algorithms are proposed and analyzed for the finite element method for the same problem with locally refined grids. The author shows that the algorithm based on the hierarchical basis decomposition converges with rate bounded by 1 - Cj- 2, where j is the number of levels. The author also analyzes the algorithm based on the full multigrid decomposition and shows that the algorithm converges with rate 1 - Cj⁻¹ for problems of any dimension. All the results are established without regularity assumption for the differential equation.