2015/12/09 by Van Tiep Chu, Chu, Van Tiep, Viet Ha Hoang +2
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1512.02788
arxiv created 2015/12/09 · openalex publication_date 2015/12/09 · arxiv updated 2015/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For two scale elliptic equations in a domain D, standard homogenization errors are deduced with the assumption that the solution u0 of the homogenized equation belongs to H2(D). For two scale Maxwell equations, the corresponding required regularity is u0∈ H1(\rm curl, D). These regularity conditions normally do not hold in general polygonal domains, which are of interests for finite element discretization. The paper establishes homogenization errors when u0 belongs to a weaker regularity space H1+s(D) for elliptic problems and Hs(\rm curl,D) for Maxwell problems where 0<s<1. Though we only present the results for two scale Maxwell equations when u0∈ Hs(\rm curl,D) with 0<s<1, the procedure works verbatim for elliptic equations when u0 belongs to H1+s(D) with 0<s<1.