An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
Xiaoting Gan ◽  
Dengguo Xu
Keyword(s):  
Differential Equations ◽  
Finite Volume ◽  
Variable Coefficient ◽  
Second Order ◽  
Volume Element ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Order Variable ◽  
Element Method

A MODIFIED IMMERSED FINITE VOLUME ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS

2020 ◽  
Vol 62 (1) ◽  
pp. 42-61
Author(s):  
Q. WANG ◽  
Z. ZHANG
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
Second Order ◽  
Volume Element ◽  
New Method ◽  
Optimal Error Estimates ◽  
Local Conservation ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Element Method

This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise $H^{2}$ regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in $L^{\infty }$ norm.

A modified immersed finite volume element method for elliptic interface problems

2020 ◽  
Vol 62 ◽  
pp. 42-61 ◽  
Author(s):  
Quanxiang Wang ◽  
Zhiyue Zhang
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
Second Order ◽  
Volume Element ◽  
New Method ◽  
Optimal Error Estimates ◽  
Local Conservation ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Element Method

This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise \(H^{2}\) regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in \(L^{\infty}\) norm. doi: 10.1017/S1446181120000073

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