A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media
An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/870402 |
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| Summary: | An approximation scheme is defined for incompressible miscible displacement
in porous media. This scheme is constructed by two methods. Under the regularity
assumption for the pressure, cubic Hermite finite element method is used for the pressure
equation, which ensures the approximation of the velocity smooth enough. A second order
characteristic finite element method is presented to handle the material derivative term of
the concentration equation. It is of second order accuracy in time increment, symmetric,
and unconditionally stable. The optimal L2-norm error estimates are derived for the scalar
concentration. |
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| ISSN: | 0161-1712 1687-0425 |