Download:
|
by Raytcho D. Lazarov, Joseph E. Pasciak, Panayot, S. Vassilevski
http://www.isc.tamu.edu/iscpubs/9903.ps
Add To MetaCart
Abstract:
Abstract. In this paper, we consider approximation of a second order elliptic problem defined on a domain in two dimensional Euclidean space. Partitioning the domain into two subdomains, we consider a technique proposed by Wieners and Wohlmuth [23] for coupling mixed finite element approximation on one subdomain with a finite element approximation on other. We consider iterative solution of the resulting linear system of equations. This system is symmetric and indefinite (of saddle-point type). The stability estimates for the discretization imply that the algebraic system can be preconditioned by a block diagonal operator involving a preconditioner for H div (on the mixed side) and one for the discrete Laplacian (on the finite element side). Alternatively, we provide iterative techniques based on domain decomposition. Utilizing subdomain solves, the composite problem is reduced to a problem defined only on the interface between the two subdomains. We prove that the interface problem is symmetric, positive definite and well conditioned and hence can be e#ectively solved by a conjugate gradient iteration. 1.
Citations
|
211
|
Non-homogeneous boundary value problems and applications
– Lions, Magenes
- 1972
|
|
120
|
A new nonconforming approach to domain decomposition: the mortar element method
– Bernardi, Maday, et al.
- 1994
|
|
112
|
A mixed finite element method for second order elliptic problems
– Raviart, Thomas
|
|
84
|
Multigrid Methods
– Bramble
- 1993
|
|
61
|
The finite element method with Lagrangian multipliers
– Babuska
- 1973
|
|
41
|
Two families of mixed elements for second order elliptic problems
– Brezzi, Douglas, et al.
- 1985
|
|
29
|
Mixed finite element methods on non-matching multiblock grids
– Arbogast, Cowsar, et al.
- 2000
|
|
21
|
Multilevel iteration for mixed finite element systems with penalty
– Cai, Goldstein, et al.
- 1993
|
|
17
|
The coupling of mixed and conforming finite element discretizations
– Wieners, Wohlmuth
- 1998
|
|
15
|
Uniform hp convergence results for the mortar finite element method
– Seshaiyer, Suri
- 1997
|
|
14
|
Mixed and Hybrid Finite Element Methods Springer-Verlag
– Brezzi, Fortin
- 1991
|
|
13
|
A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids
– Arbogast, Yotov
- 1997
|
|
12
|
Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers
– Tallec, Sassi, et al.
- 1994
|
|
11
|
A three-field domain decomposition method
– Brezzi, Marini
- 1994
|
|
9
|
Coupling finite element and spectral methods: First results
– Bernardi, Debit, et al.
- 1990
|
|
9
|
On the discretization of inter-domain coupling in elliptic boundary value problems
– Dorr
- 1989
|
|
7
|
Nonconforming matching conditions for coupling spectral finite element methods
– Bernardi, Maday, et al.
- 1989
|
|
5
|
A saddle-point principle domain decomposition method for the solution of solid mechanics problems
– Farhat
- 1991
|
|
4
|
Domain embedding preconditioners for mixed systems
– Rusten, Vassilevski, et al.
- 1997
|
|
1
|
Domain decomposition by the mortar finite element method, in Asymptotic and Numerical Methods for PDE's with Critical Parameters
– Bernardi, Maday, et al.
- 1993
|
|
1
|
A new computational approach for the linearized scalar potential formulation of the magnetostatic field problem
– Bramble, Pasciak
- 1982
|
|
1
|
Les Methodes Directes en Theorie des Equasion Elliptique
– Necas
- 1967
|
|
1
|
On two ways of stabilizing the HB multilevel methods
– Vassilevski
- 1997
|
