scholarly journals A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media

2007 ◽  
Vol 198 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Mingrong Cui
Keyword(s):  
Porous Media ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Miscible Displacement ◽  
Displacement Problem ◽  
Compressible Miscible Displacement

A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

2013 ◽  
Vol 5 (2) ◽  
pp. 163-179 ◽  
Author(s):  
Jiming Yang ◽  
Zhiguang Xiong
Keyword(s):  
Finite Element ◽  
Galerkin Method ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Mixed Finite Element ◽  
A Posteriori Error Estimates ◽  
Miscible Displacement ◽  
A Posteriori ◽  
Compressible Miscible Displacement

AbstractA kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated. The mixed finite element method is applied to the flow equation, and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method. Based on a duality argument, employing projection estimates and approximation properties, a posteriori residual-type hp error estimates for the coupled system are presented, which is often used for guiding adaptivity. Comparing with the error analysis carried out by Yang (Int. J. Numer. Meth. Fluids, 65(7) (2011), pp. 781–797), the current work is more complicated and challenging.

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