Name
Title | ||
|---|---|---|
Analysis of fully discrete FEM for miscible displacement in porous media with Bear--Scheidegger diffusion tensor. |
Abstract | ||
|---|---|---|
Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement porous media with the commonly-used Bear–Scheidegger diffusion–dispersion tensor: $$begin{aligned} D(mathbf{u}) = gamma d_m I + |mathbf{u}|bigg ( alpha _T I + (alpha _L - alpha _T) frac{mathbf{u} otimes mathbf{u}}{|mathbf{u}|^2}bigg ) , . end{aligned}$$Previous works on optimal-order (L^infty (0,T;L^2))-norm error estimate required the regularity assumption (nabla _xpartial _tD(mathbf{u}(x,t)) in L^infty (0,T;L^infty (Omega ))), while the Bear–Scheidegger diffusion–dispersion tensor is only Lipschitz continuous even for a smooth velocity field (mathbf{u}). In terms of the maximal (L^p)-regularity of fully discrete finite element solutions of parabolic equations, optimal error estimate (L^p(0,T;L^q))-norm and almost optimal error estimate (L^infty (0,T;L^q))-norm are established under the assumption of (D(mathbf{u})) being Lipschitz continuous with respect to (mathbf{u}). |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s00211-019-01030-0 | Numerische Mathematik |
Field | DocType | Volume |
Parabolic partial differential equation,Nabla symbol,Tensor,Vector field,Mathematical physics,Mathematical analysis,Galerkin method,Finite element method,Omega,Lipschitz continuity,Mathematics | Journal | 141.0 |
Issue | ISSN | Citations |
4.0 | 0945-3245 | 0 |
PageRank | References | Authors |
0.34 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wentao Cai | 1 | 0 | 0.34 |
| Buyang Li | 2 | 170 | 21.10 |
| Yanping Lin | 3 | 244 | 26.94 |
| Weiwei Sun | 4 | 154 | 15.12 |