Study of the stability and convergence of an implicit finite volume method for an spatial fractional Keller-Segel model

2017 ◽  
Author(s):  
Chahrazed Messikh
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stability And Convergence ◽  
The Stability ◽  
Volume Method

Two-Dimensional Numerical Model for Scalar Transport by Finite Volume Method on Unstructured Grid

2012 ◽  
Vol 212-213 ◽  
pp. 316-322
Author(s):  
Zhi Li Wang ◽  
Yan Fen Geng
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Grid ◽  
Transport Model ◽  
Current Model ◽  
Time Integration ◽  
Water Current ◽  
Salinity Transport ◽  
The Stability ◽  
Volume Method

Based on arbitrarily unstructured shallow water current model and finite volume method, a high-order non-oscillatory transport model is constructed. The stability and non-oscillatory condition of the transport model are also analyzed in theory. Usually, the maximum allowable time steps of current model and transport model are different, so an unsynchronized technique is used for the flow and the transport model computations to improve computational efficiency. In addition, the conservation of transport model during the unsynchronized computation is ensured by the time integration of currents continuity equation. Apply this model to the salinity transport simulation of Oujiang estuary, numerical results show that the water level, velocity and salinity agree well with the measured data.

Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

2015 ◽  
Vol 7 (4) ◽  
pp. 454-471
Author(s):  
Yanli Chen ◽  
Yonghai Li
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Stiffness Matrix ◽  
Finite Volume Methods ◽  
Matrix Analysis ◽  
Quadrilateral Meshes ◽  
Analysis Technique ◽  
The Stability ◽  
Volume Method

AbstractIn this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal convergence rate in H1 norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

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