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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| _version_ | 1832550351019966464 |
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| author | Tongjun Sun Keying Ma |
| author_facet | Tongjun Sun Keying Ma |
| author_sort | Tongjun Sun |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4e5dab8bd0de4724b1a2c018d94ce99d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4e5dab8bd0de4724b1a2c018d94ce99d2025-02-03T06:07:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/870402870402A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous MediaTongjun Sun0Keying Ma1School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaAn 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.http://dx.doi.org/10.1155/2012/870402 |
| spellingShingle | Tongjun Sun Keying Ma A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media International Journal of Mathematics and Mathematical Sciences |
| title | A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media |
| title_full | A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media |
| title_fullStr | A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media |
| title_full_unstemmed | A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media |
| title_short | A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media |
| title_sort | second order characteristic method for approximating incompressible miscible displacement in porous media |
| url | http://dx.doi.org/10.1155/2012/870402 |
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