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Volume 40, Issue 5
A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem

Hanzhang Hu & Yanping Chen

DOI: 10.4208/jcm.2101-m2020-0277

J. Comp. Math., 40 (2022), pp. 794-813.

Published online: 2022-05

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  • Abstract

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.

  • Keywords

Two-grid method, Miscible displacement problem, Mixed finite element, Characteristic finite element method.

  • AMS Subject Headings

65M06, 65M12, 65M15, 65M55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huhanzhang1016@163.com (Hanzhang Hu)

yanpingchen@scnu.edu.cn (Yanping Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-794, author = {Hu , Hanzhang and Chen , Yanping}, title = {A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {5}, pages = {794--813}, abstract = {

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2020-0277}, url = {http://global-sci.org/intro/article_detail/jcm/20548.html} }
TY - JOUR T1 - A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem AU - Hu , Hanzhang AU - Chen , Yanping JO - Journal of Computational Mathematics VL - 5 SP - 794 EP - 813 PY - 2022 DA - 2022/05 SN - 40 DO - http://doi.org/10.4208/jcm.2101-m2020-0277 UR - https://global-sci.org/intro/article_detail/jcm/20548.html KW - Two-grid method, Miscible displacement problem, Mixed finite element, Characteristic finite element method. AB -

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium. The concentration equation is treated by a mixed finite element method with characteristics (CMFEM) and the pressure equation is treated by a parabolic mixed finite element method (PMFEM). Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations. Moreover, the $L^q$ error estimates are conducted for the pressure, Darcy velocity and concentration variables in the two-grid solutions. Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.

Hu , Hanzhang and Chen , Yanping. (2022). A Characteristic Mixed Finite Element Two-Grid Method for Compressible Miscible Displacement Problem. Journal of Computational Mathematics. 40 (5). 794-813. doi:10.4208/jcm.2101-m2020-0277
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