Back to Search
Start Over
Localized harmonic characteristic basis functions for multiscale finite element methods
- Source :
- Computational and Applied Mathematics; May 2018, Vol. 37 Issue: 2 p1986-2000, 15p
- Publication Year :
- 2018
-
Abstract
- We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous coefficients. These coefficients represent the conductivity of a composite material. We assume a background with a low conductivity that contains inclusions with different thermal properties. Under this scenario, we design a multiscale finite element method to efficiently approximate solutions. The method is based on an asymptotic expansion of the solution in terms of the ratio between the conductivities. The resulting method constructs (locally) finite element basis functions (one for each inclusion). These bases generate the multiscale finite element space where the approximation of the solution is computed. Numerical experiments show the good performance of the proposed methodology.
Details
- Language :
- English
- ISSN :
- 22383603 and 18070302
- Volume :
- 37
- Issue :
- 2
- Database :
- Supplemental Index
- Journal :
- Computational and Applied Mathematics
- Publication Type :
- Periodical
- Accession number :
- ejs41568500
- Full Text :
- https://doi.org/10.1007/s40314-017-0431-3