Efficient numerical method for reliable upper and lower bounds on homogenized parameters
Abstract
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the problem and by applying the finite element method. To obtain the lower bounds we formulate the dual variational problem and introduce appropriate approximation spaces employing the finite element method as well. We deal with the 3D setting, which has been rarely considered in the literature so far. The theoretical justification of the procedure is presented and supported with illustrative examples.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Numerical methods in engineering
Composite Material Mechanics
Publication details
- Journal / source
- Computers & Mathematics with Applications
- Publisher
- Elsevier BV
- Volume
- 220
- Pages
- 219–236
- Publication date
- 10 August 2026
- Language
- EN