@misc{BankDupontYserentant, author = {Bank, Randolph and Dupont, Todd F. and Yserentant, Harry}, title = {The Hierarchical Basis Multigrid Method.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-44}, number = {SC-87-02}, abstract = {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.}, language = {en} }