TY - GEN A1 - Bank, Randolph A1 - Dupont, Todd F. A1 - Yserentant, Harry T1 - The Hierarchical Basis Multigrid Method. N2 - We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß- Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigrid V-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes. T3 - ZIB-Report - SC-87-02 KW - hierarchical basis KW - multigrid KW - finite elements KW - adaptive mesh refinement KW - preconditioned conjugate gradient methods KW - symmetric Gauss-Seidel Y1 - 1987 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44 ER -