scholarly journals Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems

2015 ◽  
Author(s):  
Jiahui Sun ◽  
Mingjuan Ma ◽  
Shichun Pang ◽  
Yongpo Zhang
Keyword(s):  
Finite Volume ◽  
Volume Element ◽  
Parabolic Problems ◽  
One Dimensional ◽  
Finite Volume Element

A Discontinuous Finite Volume Element Method Based on Bilinear Trial Functions

2017 ◽  
Vol 14 (03) ◽  
pp. 1750025 ◽  
Author(s):  
Tie Zhang ◽  
Lixin Tang
Keyword(s):  
Finite Volume ◽  
Volume Element ◽  
Parabolic Problems ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Finite Volume Element ◽  
The Stability ◽  
Bilinear Functions ◽  
First Time ◽  
Optimal Formula

We propose a discontinuous finite volume element (DFVE) method for second order elliptic and parabolic problems. Discontinuous bilinear functions are used as the trial functions. We give the stability analysis of this DFVE method and derive the optimal error estimates in the broken [Formula: see text]-norm. Specifically, the optimal [Formula: see text]-error is obtained for the first time for the bilinear DFVE methods solving elliptic and parabolic problems.

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