Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes

2009 ◽  
Vol 198 (17-20) ◽  
pp. 1638-1646 ◽  
Author(s):  
Lina Chang ◽  
Guangwei Yuan
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Diffusion Equations ◽  
Nonconforming Meshes

scholarly journals Finite volume schemes for diffusion equations: Introduction to and review of modern methods

2014 ◽  
Vol 24 (08) ◽  
pp. 1575-1619 ◽  
Author(s):  
Jerome Droniou
Keyword(s):  
Finite Volume ◽  
Approximate Solutions ◽  
Finite Volume Methods ◽  
Diffusion Equations ◽  
Maximum Principles ◽  
Finite Volume Schemes ◽  
Real World Applications ◽  
Continuous Equation ◽  
The Stability ◽  
Main Ideas

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum–maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum–maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions.

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