Name
Title | ||
|---|---|---|
Regularity of the Diffusion-Dispersion Tensor and Error Analysis of Galerkin FEMs for a Porous Medium Flow |
Abstract | ||
|---|---|---|
We study Galerkin finite element methods for an incompressible miscible flow in porous media with the commonly used Bear-Scheidegger diffusion-dispersion tensor D(u) = Phi d(m)I+ vertical bar u vertical bar(alpha I-T + (alpha(L) - alpha T)(vertical bar u vertical bar 2)(u circle times u)). The traditional approach to optimal L infinity((0, T); L-2) error estimates is based on an elliptic Ritz projection, which usually requires the regularity of del(x)partial derivative D-t(u(x, t)) is an element of L-p(Omega(T)). However, the Bear-Scheidegger diffusion-dispersion tensor may not satisfy the regularity condition even for a smooth velocity field u. A new approach is presented in this paper, in terms of a parabolic projection, which only requires the Lipschitz continuity of D(u). With the new approach, we establish optimal L-p error estimates and an almost optimal L-infinity error estimate. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140958803 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
parabolic projection,L-p stability,diffusion-dispersion tensor,porous medium flow,Galerkin FEM,error analysis | Mathematical optimization,Nabla symbol,Tensor,Mathematical analysis,Vector field,Galerkin method,Finite element method,Omega,Lipschitz continuity,Mathematics,Parabola | Journal |
Volume | Issue | ISSN |
53 | 3 | 0036-1429 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Buyang Li | 1 | 170 | 21.10 |
| Weiwei Sun | 2 | 154 | 15.12 |