-
Views
-
Cite
Cite
Xuejun Xu, S. H. Lui, T. Rahman, A two‐level additive Schwarz method for the Morley nonconforming element approximation of a nonlinear biharmonic equation, IMA Journal of Numerical Analysis, Volume 24, Issue 1, January 2004, Pages 97–122, https://doi.org/10.1093/imanum/24.1.97
- Share Icon Share
Abstract
In this paper, we consider the well known Morley nonconforming element approximation of a nonlinear biharmonic equation which is related to the well‐known two‐dimensional Navier–Stokes equations. Firstly, optimal energy and H1‐norm estimates are obtained. Secondly, a two‐level additive Schwarz method is presented for the discrete nonlinear algebraic system. It is shown that if the Reynolds number is sufficiently small, the two‐level Schwarz method is optimal, i.e. the convergence rate of the Schwarz method is independent of the mesh size and the number of subdomains.