Abstract
In this paper, we consider multiscale approaches for solving parabolic equations with heterogeneous coefficients. Our interest stems from porous media applications and we assume that there is no scale separation with respect to spatial variables. To compute the solution of these multiscale problems on a coarse grid, we define global fields such that the solution smoothly depends on these fields. We present various finite element discretization techniques and provide analyses of these methods. A few representative numerical examples are presented using heterogeneous fields with strong non-local features. These numerical results demonstrate that the solution can be captured more accurately on the coarse grid when some type of limited global information is used.
Original language | English (US) |
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Pages (from-to) | 833-859 |
Number of pages | 27 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2007 |
Externally published | Yes |
Keywords
- Continuum scale
- Global information
- Multiscale methods
- Parabolic equations
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics