2024/03/25 by Antônio Tadeu A. Gomes, Gomes, Antônio Tadeu Azevedo, Weslley da Silva Pereira +3
Computer Science · Engineering · #65N12 #65N22 #65N30 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2403.16890
openalex publication_date 2024/03/25 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/30
The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the linear elasticity problem which are free from Poisson locking. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient refinement levels on the fine-scale mesh such that the MHM method is well-posed, optimally convergent under local regularity conditions, and locking-free. Two-dimensional numerical tests assess theoretical results.