ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

2013 ◽  
Vol 04 (03) ◽  
pp. 1350013 ◽  
Author(s):  
SARVESH KUMAR
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
A Priori ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Miscible Displacement ◽  
Volume Element ◽  
Finite Volume Element ◽  
Velocity Equation ◽  
Concentration Equation

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure–velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

scholarly journals Modified Method of Characteristics Combined with Finite Volume Element Methods for Incompressible Miscible Displacement Problems in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Sarvesh Kumar ◽  
Sangita Yadav
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Method Of Characteristics ◽  
Miscible Displacement ◽  
Volume Element ◽  
Modified Method ◽  
Finite Volume Element ◽  
Velocity Equation ◽  
Modified Method Of Characteristics ◽  
Concentration Equation

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation. Since modified method of characteristics (MMOC) minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in L∞(L2) norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

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 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 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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