TY - JOUR
T1 - An expanded mixed finite element method for generalized Forchheimer flows in porous media
AU - Ibragimov, Akif
AU - Kieu, Thinh T.
N1 - Funding Information:
This work was supported by National Science Foundation grant (DMS, Award # 1422796 ).
Publisher Copyright:
© 2016 Elsevier Ltd
PY - 2016/9/1
Y1 - 2016/9/1
N2 - We study the expanded mixed finite element method applied to degenerate parabolic equations with the Dirichlet boundary condition. The equation is considered a prototype of the nonlinear Forchheimer equation for slightly compressible fluid flow in porous media. The bounds for the solutions are established. In both continuous and discrete time procedures, utilizing the monotonicity properties of Forchheimer equation and the boundedness of solutions, we establish the error estimates in L2-norm for solutions, divergence of the vector variable in several Lebesgue norms. A numerical example using the lowest order Raviart–Thomas (RT0) mixed element confirms our theoretical results regarding convergence rates.
AB - We study the expanded mixed finite element method applied to degenerate parabolic equations with the Dirichlet boundary condition. The equation is considered a prototype of the nonlinear Forchheimer equation for slightly compressible fluid flow in porous media. The bounds for the solutions are established. In both continuous and discrete time procedures, utilizing the monotonicity properties of Forchheimer equation and the boundedness of solutions, we establish the error estimates in L2-norm for solutions, divergence of the vector variable in several Lebesgue norms. A numerical example using the lowest order Raviart–Thomas (RT0) mixed element confirms our theoretical results regarding convergence rates.
KW - Error estimates
KW - Expanded mixed finite element
KW - Generalized Forchheimer equations
KW - Nonlinear degenerate parabolic equations
UR - http://www.scopus.com/inward/record.url?scp=84994850615&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2016.06.029
DO - 10.1016/j.camwa.2016.06.029
M3 - Article
AN - SCOPUS:84994850615
SN - 0898-1221
VL - 72
SP - 1467
EP - 1483
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 6
ER -