ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65F10, 65N20
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. We develop and analyze a procedure for creating a hierarchical basis of continuous piecewise linear polynomials on an arbitrary, unstructured, nonuniform triangular mesh. Using these hierarchical basis functions, we are able to define and analyze corresponding iterative methods for solving the linear systems arising from finite element discretizations of elliptic partial differential equations. We show that such iterative methods perform as well as those developed for the usual case of structured, locally refined meshes. In particular, we show that the generalized condition numbers for such iterative methods are of order $J^2$ , where $J$ is the number of hierarchical basis levels.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050181
