scholarly journals Superconvergence and asymptotic expansions for bilinear finite volume element approximation on non-uniform grids

2017 ◽  
Vol 321 ◽  
pp. 323-335
Author(s):  
Cunyun Nie ◽  
Shi Shu ◽  
Haiyuan Yu ◽  
Wenhua Xia
Keyword(s):  
Finite Volume ◽  
Asymptotic Expansions ◽  
Volume Element ◽  
Element Approximation ◽  
Uniform Grids ◽  
Finite Volume Element

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.

scholarly journals Finite Volume Element Approximation for the Elliptic Equation with Distributed Control

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Quanxiang Wang ◽  
Tengjin Zhao ◽  
Zhiyue Zhang
Keyword(s):  
Finite Volume ◽  
Optimal Control Problems ◽  
A Priori ◽  
Elliptic Partial Differential Equation ◽  
Volume Element ◽  
Element Approximation ◽  
Element Formulation ◽  
Variational Discretization ◽  
Finite Volume Element ◽  
Priori Error Estimates

In this paper, we consider a priori error estimates for the finite volume element schemes of optimal control problems, which are governed by linear elliptic partial differential equation. The variational discretization approach is used to deal with the control. The error estimation shows that the combination of variational discretization and finite volume element formulation allows optimal convergence. Numerical results are provided to support our theoretical analysis.

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