THE EFFECT OF NUMERICAL INTEGRATION IN MIXED METHODS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT WHEN MOLECULAR DISPERSION IS INCLUDED

2017 ◽  
Vol 15 (4) ◽  
pp. 305-332
Author(s):  
Nguimbi Germain ◽  
Pongui Ngoma Diogène Vianney ◽  
Likibi Pellat Rhoss Beauneur
Keyword(s):  
Mixed Methods ◽  
Numerical Integration ◽  
Miscible Displacement ◽  
Molecular Dispersion ◽  
Compressible Miscible Displacement ◽  
Effect Of Numerical Integration

scholarly journals The effect of numerical integration in mixed finite element approximation in the simulation of miscible displacement

2017 ◽  
Vol 6 (2) ◽  
pp. 44
Author(s):  
Pongui ngoma Diogene Vianney ◽  
Nguimbi Germain ◽  
Likibi Pellat Rhoss Beaunheur
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Mixed Finite Element ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Miscible Displacement ◽  
Optimal Order ◽  
Element Approximation ◽  
Quadrature Scheme ◽  
Effect Of Numerical Integration

We consider the effect of numerical integration in finite element  procedures applied to a nonlinear system of two coupled partial differential equations describing the miscible displacement of one incompressible fluid by another in a porous meduim. We consider the use of the numerical quadrature scheme for approximating the pressure and velocity by a mixed method using Raviart - Thomas space of index  and the concentration by a standard Galerkin method. We also give some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal order estimates are derived when the imposed external flows are smoothly distributed.

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