3. Finite Difference and Finite Volume Methods

2008 ◽  
pp. 91-134
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Finite Volume Methods

COMPARISON OF FINITE VOLUME AND FINITE DIFFERENCE METHODS AND APPLICATION

2006 ◽  
Vol 04 (02) ◽  
pp. 163-208 ◽  
Author(s):  
S. FAURE ◽  
D. PHAM ◽  
R. TEMAM
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Finite Volume ◽  
Finite Difference Methods ◽  
Finite Volume Methods ◽  
Uniform Grid ◽  
Parabolic Boundary ◽  
Convergence Results ◽  
Difference Methods ◽  
Parabolic Boundary Value Problems

In this article, we consider finite volume methods based on a non-uniform grid. Finite volume methods are compared to finite difference methods based on a related grid. As an application, various convergence results are proved for the finite volume function spaces and for some model elliptic and parabolic boundary value problems using these discretization spaces.

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