A Multi-Level-Algorithm for the Solution of Second Order
        Elliptic Differential Equations on Sparse Grids

                      Christoph Pflaum
     Institut f"ur Informatik, Technische Universit"at M"unchen
                D-80290 M"unchen, Germany
          e-mail: pflaum@informatik.tu-muenchen.de


A  multilevel algorithm is presented that solves general second order
elliptic partial differential equations on adaptive sparse grids.
The multilevel algorithm consists of several V-cycles.
Suitable discretizations provide that the discrete equation system 
can be solved in an efficient way. 
Numerical experiments show a convergence rate of order $O(1)$ for the
multilevel algorithm.