Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs

Authors

Messaoud Boulbrachene, Department of Mathematics, Sultan Qaboos University, P.O. Box 36, PC 123, Al- Khoud, Muscat Sultanate of Oman.

Abstract

In this paper, we prove uniform convergence of the standard finite element method for a Schwarz alternating procedure for nonlinear elliptic partial differential equations in the context of linear subdomain problems and nonmatching grids. The method stands on the combination of the convergence of linear Schwarz sequences with standard finite element L-error estimate for linear problems.

Recommended Citation

Boulbrachene, Messaoud (2019) Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs, Sultan Qaboos University Journal For Science: Vol. 24: Iss. 2, 109-121.
DOI: https://doi.org/10.24200/squjs.vol24iss2pp109-121
Available at: https://squjs.squ.edu.om/squjs/vol24/iss2/4