Volume 9, Issue 1
An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow

H. Chen, Z. Zhou & H. Wang

Int. J. Numer. Anal. Mod., 9 (2012), pp. 132-148.

Published online: 2012-09

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  • Abstract

We present an $H^1$-Galerkin mixed finite element method for the solution of a nonlinear parabolic pressure equation, which arises in the mathematical models for describing a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal-order error estimate for the method. Numerical experiments are performed to justify the theoretical analysis.

  • Keywords

$H^1$-Galerkin mixed finite element method, optimal-order error estimates, numerical examples.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-132, author = {}, title = {An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {132--148}, abstract = {

We present an $H^1$-Galerkin mixed finite element method for the solution of a nonlinear parabolic pressure equation, which arises in the mathematical models for describing a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal-order error estimate for the method. Numerical experiments are performed to justify the theoretical analysis.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/616.html} }
TY - JOUR T1 - An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 132 EP - 148 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/616.html KW - $H^1$-Galerkin mixed finite element method, optimal-order error estimates, numerical examples. AB -

We present an $H^1$-Galerkin mixed finite element method for the solution of a nonlinear parabolic pressure equation, which arises in the mathematical models for describing a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal-order error estimate for the method. Numerical experiments are performed to justify the theoretical analysis.

H. Chen, Z. Zhou & H. Wang. (2019). An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow. International Journal of Numerical Analysis and Modeling. 9 (1). 132-148. doi:
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