scholarly journals A matching of singularities in domain decomposition methods for reaction-diffusion problems with discontinuous coefficients

2010 ◽  
Vol 45 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Chokri Chniti
Keyword(s):  
Domain Decomposition ◽  
Reaction Diffusion ◽  
Decomposition Methods ◽  
Discontinuous Coefficients ◽  
Domain Decomposition Methods ◽  
Diffusion Problems

A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems

2015 ◽  
Vol 18 (2) ◽  
pp. 297-320
Author(s):  
Xingding Chen ◽  
Guangwei Yuan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maximum Principle ◽  
Domain Decomposition ◽  
Decomposition Methods ◽  
Discontinuous Coefficients ◽  
Discrete Maximum Principle ◽  
Diffusion Tensors ◽  
Diffusion Problems ◽  
Element Method

AbstractIn this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

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