Domain decomposition based iterative methods for nonlinear elliptic finite element problems
1994
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Keywords:
- Mixed finite element method
- Extended finite element method
- Mathematical optimization
- Domain decomposition methods
- Mortar methods
- Finite element method
- Schwarz alternating method
- Additive Schwarz method
- Mathematics
- Numerical partial differential equations
- Discrete mathematics
- Discontinuous Galerkin method
- hp-FEM
- Applied mathematics
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
0
References
0
Citations
NaN
KQI