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.

A Priori Error Estimates of Crank-Nicolson Finite Volume Element Method for Parabolic Optimal Control Problems

2013 ◽  
Vol 5 (05) ◽  
pp. 688-704 ◽  
Author(s):  
Xianbing Luo ◽  
Yanping Chen ◽  
Yunqing Huang
Keyword(s):  
Optimal Control ◽  
Finite Volume ◽  
Optimal Control Problems ◽  
A Priori ◽  
Volume Element ◽  
Control Problems ◽  
Finite Volume Element Method ◽  
Finite Volume Element ◽  
Element Method ◽  
Crank Nicolson

AbstractIn this paper, the Crank-Nicolson linear finite volume element method is applied to solve the distributed optimal control problems governed by a parabolic equation. The optimal convergent orderO(h2+k2) is obtained for the numerical solution in a discreteL2-norm. A numerical experiment is presented to test the theoretical result.

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.

A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

2014 ◽  
Vol 6 (5) ◽  
pp. 615-636 ◽  
Author(s):  
Zhendong Luo
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Stokes Equations ◽  
Volume Element ◽  
Navier Stokes ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Fully Discrete ◽  
Finite Volume Element ◽  
Stationary Navier Stokes Equations

AbstractA semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.

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