A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media
Document Type
Article
Publication Date
11-2014
Department
Department of Mathematical Sciences
Abstract
A combined method consisting of the mixed finite element method for flow and the local discontinuous Galerkin method for transport is introduced for the one-dimensional coupled system of incompressible miscible displacement problem. Optimal error estimates in L∞(0, T;L2) for concentration c, in L2(0, T; L2) for cxand L∞(0, T;L2) for velocity u are derived. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. Numerical experiments are performed to verify the theoretical results. Finally, we apply this method to the one-dimensional compressible miscible displacement problem and give the numerical experiments to confirm the efficiency of the scheme.
Publication Title
Science China Mathematics
Recommended Citation
Guo, H.,
Zhang, Q.,
&
Yang, Y.
(2014).
A combined mixed finite element method and local discontinuous Galerkin method for miscible displacement problem in porous media.
Science China Mathematics,
57(11), 2301-2320.
http://doi.org/10.1007/s11425-014-4879-y
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5042