A numerical method is formulated and analyzed for solving the miscible displacement problem under low regularity assumptions. The scheme employs discontinuous Galerkin time stepping with mixed and interior penalty discontinuous Galerkin finite elements in space. The numerical approximations of the pressure, velocity, and concentration converge to the weak solution as the mesh size and time step tend to zero. To pass to the limit a compactness theorem is developed which generalizes the Aubin−Lions theorem to accommodate discontinuous functions both in space and in time.
DOI : 10.1051/m2an/2014059
Mots clés : Generalized Aubin−Lions, discontinuous Galerkin, mixed finite element, arbitrary order, weak solution, convergence
@article{M2AN_2015__49_4_953_0,
author = {Li, Jizhou and Riviere, Beatrice and Walkington, Noel},
title = {Convergence of a high order method in time and space for the miscible displacement equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {953--976},
publisher = {EDP-Sciences},
volume = {49},
number = {4},
year = {2015},
doi = {10.1051/m2an/2014059},
mrnumber = {3371899},
zbl = {1327.65176},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014059/}
}
TY - JOUR AU - Li, Jizhou AU - Riviere, Beatrice AU - Walkington, Noel TI - Convergence of a high order method in time and space for the miscible displacement equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 953 EP - 976 VL - 49 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014059/ DO - 10.1051/m2an/2014059 LA - en ID - M2AN_2015__49_4_953_0 ER -
%0 Journal Article %A Li, Jizhou %A Riviere, Beatrice %A Walkington, Noel %T Convergence of a high order method in time and space for the miscible displacement equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 953-976 %V 49 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014059/ %R 10.1051/m2an/2014059 %G en %F M2AN_2015__49_4_953_0
Li, Jizhou; Riviere, Beatrice; Walkington, Noel. Convergence of a high order method in time and space for the miscible displacement equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 953-976. doi : 10.1051/m2an/2014059. http://www.numdam.org/articles/10.1051/m2an/2014059/
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