Modified method of characteristics combined with finite volume element methods for incompressible miscible displacement problems in porous media
type: Item
instance of: scholarly article
title: Modified method of characteristics combined with finite volume element methods for incompressible miscible displacement problems in porous media
zbMATH Open document ID: 1426.76391
DOI: 10.1155/2014/245086
author: Sarvesh Kumar
author: Sangita Yadav
published in: International Journal of Partial Differential Equations
publication date: 2014-09-30T00:00:00Z
review text: Summary: 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 \(L^{\infty}(L^2)\) norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 6349583
Wikidata QID: Q59049106
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/245086
OpenAlex ID: W2089784552
cites work: Mathematical Analysis for Reservoir Models
cites work: On existence and uniqueness results for a coupled systems modeling miscible displacement in porous media
cites work: Numerical Approximations for a Miscible Displacement Process in Porous Media
cites work: The approximation of the pressure by a mixed method in the simulation of miscible displacement
cites work: A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
cites work: Galerkin Methods for Miscible Displacement Problems in Porous Media
cites work: A mixed and discontinuous Galerkin finite volume element method for incompressible miscible displacement problems in porous media
cites work: Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
cites work: Some Improved Error Estimates for the Modified Method of Characteristics
cites work: On the Approximation of Miscible Displacement in Porous Media by a Method of Characteristics Combined with a Mixed Method
cites work: Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
cites work: Mixed Covolume Methods on Rectangular Grids For Elliptic Problems
cites work: Mixed Covolume Methods for Elliptic Problems on Triangular Grids
cites work: Some Error Estimates for the Box Method
cites work: On the finite volume element method
cites work: Finite Volume Methods for Elliptic PDE's: A New Approach
cites work: Q5439738
cites work: Galerkin finite element methods for parabolic problems
cites work: Mixed and Hybrid Finite Element Methods
cites work: A finite volume method based on the Crouzeix-Raviart element for elliptic PDE's in two dimensions
cites work: Q4162607
cites work: Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
cites work: Q4936091
cites work: On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
cites work: Q4663883
cites work: Efficient Time-Stepping Methods for Miscible Displacement Problems in Porous Media
cites work: An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian--Lagrangian Localized Adjoint Method and Mixed Finite Element Methods
cites work: Finite Volume Approximations for Incompressible Miscible Displacement Problems in Porous Media with Modified Method of Characteristics
description: scientific article; zbMATH DE number 6349583