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 |
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Pages (from-to) | 353–397 |
Number of pages | 45 |
Journal | Numerische Mathematik |
Volume | 141 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2019 |