scholarly journals Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

2011 ◽  
Vol 4 (3) ◽  
pp. 319-334 ◽  
Author(s):  
Weizhang Huang
Keyword(s):  
Finite Element ◽  
Maximum Principle ◽  
Anisotropic Diffusion ◽  
Discrete Maximum Principle ◽  
Two Dimensional ◽  
Finite Element Approximations ◽  
Linear Finite Element ◽  
Mesh Condition ◽  
Diffusion Problems

Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems

2014 ◽  
Vol 6 (06) ◽  
pp. 849-866
Author(s):  
Xingding Chen ◽  
Guangwei Yuan ◽  
Yunlong Yu
Keyword(s):  
Finite Element ◽  
Maximum Principle ◽  
Anisotropic Diffusion ◽  
Computational Cost ◽  
Discrete Maximum Principle ◽  
Local Repair ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Repair Technique ◽  
Repair Techniques

AbstractIn this paper, we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle. It is an extension of the existing local repair technique. Both of the repair techniques preserve the total energy and are easy to be implemented. The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme, and the computational cost of the global repair technique is cheaper than the local repair technique when the diffusion tensors are highly anisotropic.

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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