Additive Schwarz algorithms for parabolic convection-diffusion equations

Babuška, I. (1972): The mathematical foundations of the finite element method, with applications to partial differential equations, A.D. Aziz ed. Academic Press, New York London Bjørstad, P.E., Widlund, O.B. (1986): Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal.23, 1093–1120 Bramble, J.H. (1966): A second order finite difference analogue of the first biharmonic boundary value problem. Numer. Math.9, 236–249 Bramble, J.H., Pasciak, J.E., Schatz, A.H. (1986): The construction of preconditioners for elliptic problems by substructuring, I. Math. Comput.47, 103–134 Bramble, J.H., Pasciak, J.E., Schatz, A.H. (1987): The construction of preconditioners for elliptic problems by substructuring, II. Math. Comput.49, 1–16 Bramble, J.H., Pasciak, J.E., Schatz, A.H. (1988): The construction of preconditioners for elliptic problems by substructuring, III. Math. Comput.51, 415–430 Bramble, J.H., Pasciak, J.E., Shatz, A.H. (1989): The construction of preconditoners for elliptic problems by substructuring, IV. Math. Comput.53, 1–24 Cai, X.-C. (1989): Some domain decomposition algorithms for nonselfadjoint elliptic and parabolic partial differential equations. Ph.D. thesis, Courant Institute Cai, X.-C. (1990): An additive Schwarz algorithm for nonselfadjoint elliptic equations. In: T. Chan, R. Glowinski, J. Périaux, O. Widlund, eds., Third International, Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia Cai, X.-C., Widlund, O.B. (1990): Multiplicative Schwarz algorithms for nonsymmetric and indefinite elliptic and parabolic problems. Tech. Rep. CCS-90-7, Center for Comput. Sci., Univ. of Kentucky Dawson, C., Du, Q. Dupont, T.F., (1989): A finite difference domain decomposition algorithm for numerical solution of the heat equation. Tech. Rep., 89–09, Univ. of Chicago Dryja, M. (1989): An additive Schwarz algorithm for two-and three-dimensional finite element elliptic problems. In: T. Chan, R. Glowinski, G.A. Meurant, J. Périaux, O. Widlund, eds., Domain Decomposition Methods for Partial Differential Equations II. Philadelphia Dryja, M., Widlund, O.B. (1987): An additive variant of the Schwarz alternating method for the case of many subregions. Tech. Rep. 339, Dept. of Comp. Sci., Courant Institute Dryja, M., Widlund, O.B. (1989): Some domain decomposition algorithms for elliptic problems. In: L. Hayes, D. Kincaid, eds., Iterative Methods for Large Linear Systems. Academic Press, San Diego California Dryja, M., Widlund, O.B. (1990): Towards a unified theory of domain decomposition algorithms for elliptic problems. In: T. Chan, R. Glowinski, J. Périaux, O. Widlund, eds., Third International Symposium on Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia Eisenstat, S.C., Elman, H.C., Schultz, M.H. (1983): Variational iterative methods for nonsymmetric system of linear equations. SIAM J. Numer. Anal.20, 345–357 Ewing, R.E., Lazarov, R.D., Pasciak, J.E., Vassilevski, P.S. (1989): Finite element methods for parabolic problems with time steps variable in space. Tech. Rep. # 1989-05, Inst. for Sci. Comp., Univ. of Wyoming Grisvard, P. (1985): Elliptic Problems in Nonsmooth Domains. Pitman, Boston, MA Johnson, C. (1987): Numerical Solution of Partial Differential Equation by the Finite Element Method. Cambridge University Press, Cambridge Kuznetsov, Yu.A. (1989): Domain decomposition methods for time-dependent problems. Preprint Lions, P.L. (1988): On the Schwarz alternating method. I. In: R. Glowinski, G. H. Golub, G. A. Meurant, J. Périaux, eds., Domain Decomposition Methods for Partial Differential Equations. SIAM, Philadelphia Nečas, J. (1964): Sur la Coercivité des Formes Sesquilinéaires, Elliptiques. Rev. Roumaine Math. Pures Appl.9, 47–69 Saad, Y., Schultz, M.H. (1986): GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp.7, 865–869 Yserentant, H. (1986): On the multi-level splitting of finite element spaces. Numer Math.49, 379–412