2017/02/10 by Michael Eden, Adrian Muntean, Eden, Michael +1
Computer Science · Engineering · #35B27 (Primary) #35B40 #74F05 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1702.03247
openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 an earlier paper 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.