Michael Eden, Adrian Muntean
Abstract:
We investigate corrector estimates for the solutions of a thermoelasticity
problem posed in a highly heterogeneous two-phase medium and its
corresponding two-scale thermoelasticity model which was derived in [11]
by two-scale convergence arguments.
The medium in question consists of a connected matrix with disconnected,
initially periodically distributed inclusions separated by a sharp interface
undergoing a priori known phase transformations.
While such estimates seem not to be obtainable in the fully coupled setting,
we show that for some simplified scenarios optimal convergence rates can be
proven rigorously.
The main technique for the proofs are energy estimates using special
reconstructions of two-scale functions and particular operator estimates for
periodic functions with zero average.
Here, additional regularity results for the involved functions are necessary.
Submitted February 12, 2017. Published February 23, 2017.
Math Subject Classifications: 35B27, 35B40, 74F05.
Key Words: Homogenization; two-phase thermoelasticity; corrector estimates;
time-dependent domains; distributed microstructures.
Show me the PDF file (346 KB), TEX file for this article.
 |
Michael Eden Center for Industrial Mathematics, FB 3 University of Bremen Bibliotheksstr. 1, 28359 Bremen, Germany email: leachim@math.uni-bremen.de |
|---|---|
 |
Adrian Muntean Department of Mathematics and Computer Science University of Karlstad Universitetsgatan 2 651 88 Karlstad, Sweden email: adrian.muntean@kau.se |
Return to the EJDE web page