A finite volume element method for a non-linear elliptic problem

2005 ◽  
Vol 12 (5-6) ◽  
pp. 515-546 ◽  
Author(s):  
P. Chatzipantelidis ◽  
V. Ginting ◽  
R. D. Lazarov
Keyword(s):  
Finite Volume ◽  
Elliptic Problem ◽  
Volume Element ◽  
Finite Volume Element Method ◽  
Non Linear ◽  
Finite Volume Element ◽  
Linear Elliptic Problem ◽  
Element Method

A Stabilized Finite Volume Element Method for Stationary Stokes–Darcy Equations Using the Lowest Order

2019 ◽  
Vol 17 (08) ◽  
pp. 1950053
Author(s):  
Yanyun Wu ◽  
Liquan Mei ◽  
Meilan Qiu ◽  
Yuchuan Chu
Keyword(s):  
Finite Volume ◽  
Mass Conservation ◽  
Volume Element ◽  
Optimal Error Estimates ◽  
Irregular Domain ◽  
Finite Volume Element Method ◽  
Stabilized Finite Element Method ◽  
Finite Volume Element ◽  
Text Element ◽  
Element Method

We present a stabilized finite volume element method for the coupled Stokes–Darcy problem with the lowest order [Formula: see text] element for the Stokes region and [Formula: see text] element for the Darcy region. Based on adding a jump term of discrete pressure to the approximation equation, a discrete inf-sup condition is established for the proposed method. The optimal error estimates in the [Formula: see text]-norm for the velocity and piezometric head and in the [Formula: see text]-norm for the pressure are proved. And they are also verified through some numerical experiments. Two figures are given to show the full comparison for the local mass conservation between the proposed method and the stabilized finite element method. And this method can also be computed directly in the irregular domain according to the last experiment.

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