ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 65F10, 65N30, 65N55
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. Multilevel Schwarz methods are developed for a conforming finite element approximation of second order elliptic problems. We focus on problems in three dimensions with possibly large jumps in the coefficients across the interface separating the subregions. We establish a condition number estimate for the iterative operator, which is independent of the coefficients, and grows at most as the square of the number of levels. We also characterize a class of distributions of the coefficients, called quasi-monotone, for which the weighted $L^{2}$ -projection is stable and for which we can use the standard piecewise linear functions as a coarse space. In this case, we obtain optimal methods, i.e. bounds which are independent of the number of levels and subregions. We also design and analyze multilevel methods with new coarse spaces given by simple explicit formulas. We consider nonuniform meshes and conclude by an analysis of multilevel iterative substructuring methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050172
Permalink