Skip to main content
Log in

Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received April 6, 1994 / Revised version received December 7, 1994

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dryja, M., Sarkis, M. & Widlund, O. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions . Numer. Math. 72, 313–348 (1996). https://doi.org/10.1007/s002110050172

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002110050172

Navigation