Finite volume element approximation for nonlinear diffusion problems with degenerate diffusion coefficients

2019 ◽  
Vol 140 ◽  
pp. 23-47 ◽  
Author(s):  
Dan Wu ◽  
Jingyan Yue ◽  
Guangwei Yuan ◽  
Junliang Lv
Keyword(s):  
Finite Volume ◽  
Diffusion Coefficients ◽  
Nonlinear Diffusion ◽  
Volume Element ◽  
Element Approximation ◽  
Degenerate Diffusion ◽  
Finite Volume Element ◽  
Diffusion Problems

scholarly journals A Fully Discrete Symmetric Finite Volume Element Approximation of Nonlocal Reactive Flows in Porous Media

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Zhe Yin ◽  
Qiang Xu
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Volume Element ◽  
Optimal Order ◽  
Element Approximation ◽  
Two Dimensional ◽  
Reactive Flows ◽  
Flows In Porous Media ◽  
Fully Discrete ◽  
Finite Volume Element

We study symmetric finite volume element approximations for two-dimensional parabolic integrodifferential equations, arising in modeling of nonlocal reactive flows in porous media. It is proved that symmetric finite volume element approximations are convergent with optimal order inL2-norm. Numerical example is presented to illustrate the accuracy of our method.

scholarly journals Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

2017 ◽  
Vol 27 (3) ◽  
pp. 515-525 ◽  
Author(s):  
Jin-Liang Yan ◽  
Liang-Hong Zheng
Keyword(s):  
Finite Volume ◽  
Vries Equation ◽  
Numerical Study ◽  
Volume Element ◽  
Element Approximation ◽  
Element Scheme ◽  
De Vries ◽  
Long Time ◽  
Discrete Variational Derivative Method ◽  
Finite Volume Element

AbstractThe aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg–de Vries equation.

Sign in / Sign up

Export Citation Format

Share Document