Abstract
We analyse the convergence of numerical schemes in the GDM–ELLAM (Gradient Discretisation Method–Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elliptic-parabolic PDE which models miscible displacement in porous media. These schemes include, but are not limited to, Mixed Finite Element–ELLAM and Hybrid Mimetic Mixed–ELLAM schemes. A complete convergence analysis is presented on the coupled model, using only weak regularity assumptions on the solution (which are satisfied in practical applications), and not relying on L∞ bounds (which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications).
| Original language | English |
|---|---|
| Pages (from-to) | 353–397 |
| Number of pages | 45 |
| Journal | Numerische Mathematik |
| Volume | 141 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Feb 2019 |
Cite this
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Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media. / Cheng, Hanz Martin; Droniou, Jérôme; Le, Kim Ngan.
In: Numerische Mathematik, Vol. 141, No. 2, 02.2019, p. 353–397.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media
AU - Cheng, Hanz Martin
AU - Droniou, Jérôme
AU - Le, Kim Ngan
PY - 2019/2
Y1 - 2019/2
N2 - We analyse the convergence of numerical schemes in the GDM–ELLAM (Gradient Discretisation Method–Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elliptic-parabolic PDE which models miscible displacement in porous media. These schemes include, but are not limited to, Mixed Finite Element–ELLAM and Hybrid Mimetic Mixed–ELLAM schemes. A complete convergence analysis is presented on the coupled model, using only weak regularity assumptions on the solution (which are satisfied in practical applications), and not relying on L∞ bounds (which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications).
AB - We analyse the convergence of numerical schemes in the GDM–ELLAM (Gradient Discretisation Method–Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elliptic-parabolic PDE which models miscible displacement in porous media. These schemes include, but are not limited to, Mixed Finite Element–ELLAM and Hybrid Mimetic Mixed–ELLAM schemes. A complete convergence analysis is presented on the coupled model, using only weak regularity assumptions on the solution (which are satisfied in practical applications), and not relying on L∞ bounds (which are impossible to ensure at the discrete level given the anisotropic diffusion tensors and the general grids used in applications).
UR - http://www.scopus.com/inward/record.url?scp=85055543403&partnerID=8YFLogxK
U2 - 10.1007/s00211-018-1002-2
DO - 10.1007/s00211-018-1002-2
M3 - Article
VL - 141
SP - 353
EP - 397
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 2
ER -