AN ALGORITHM FOR COARSENING UNSTRUCTURED MESHES

We develop and analyze a procedure for creating a hierarchical basis o f continuous piecewise linear polynomials on an arbitrary, unstructure d, nonuniform triangular mesh. Using these hierarchical basis function s, we are able to define and analyze corresponding iterative methods f or solving the linear systems arising from finite element discretizati ons of elliptic partial differential equations. We show that such iter ative methods perform as well as those developed for the usual case of structured, locally refined meshes. In particular, we show that the g eneralized condition numbers for such iterative methods are of order J (2), where J is the number of hierarchical basis levels.