scholarly journals A non-overlapping domain decomposition method for continuous-pressure mixed finite element approximations of the Stokes problem

2010 ◽  
Vol 45 (4) ◽  
pp. 675-696 ◽  
Author(s):  
Hani Benhassine ◽  
Abderrahmane Bendali
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Stokes Problem ◽  
Mixed Finite Element ◽  
Finite Element Approximations ◽  
Overlapping Domain Decomposition

A Non-Overlapping Domain Decomposition Method for the Stokes Problem

2002 ◽  
Author(s):  
Attila Zsaki ◽  
Marius Paraschivoiu
Keyword(s):  
Domain Decomposition ◽  
Lagrange Multipliers ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Stokes Problem ◽  
Uzawa Algorithm ◽  
Driven Cavity ◽  
Numerical Tests ◽  
Overlapping Domain Decomposition ◽  
The Cost

A domain decomposition method for the Stokes problem using Lagrange multipliers is described. The dual system associated with the Lagrange multipliers is solved based on an iterative procedure using the two-level finite element tearing and interconnecting (FETI) method. Numerical tests are performed by solving the driven cavity problem. An analysis of the number of outer iterations and an evaluation of the cost of the inner iterations are reported. Comparison with the well-known Uzawa algorithm shows a reduction in the floating point operations count of the inner iterations while achieving the same number of outer iterations.

scholarly journals Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients

2018 ◽  
Vol 52 (5) ◽  
pp. 2003-2035
Author(s):  
P. Ciarlet ◽  
L. Giret ◽  
E. Jamelot ◽  
F.D. Kpadonou
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Source Term ◽  
Domain Decomposition Method ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Different Characteristics

We study first the convergence of the finite element approximation of the mixed diffusion equations with a source term, in the case where the solution is of low regularity. Such a situation commonly arises in the presence of three or more intersecting material components with different characteristics. Then we focus on the approximation of the associated eigenvalue problem. We prove spectral correctness for this problem in the mixed setting. These studies are carried out without, and then with a domain decomposition method. The domain decomposition method can be non-matching in the sense that the traces of the finite element spaces may not fit at the interface between subdomains. Finally, numerical experiments illustrate the accuracy of the method.

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