2024/01/26 by Hongpeng Li, Li Xu, Li, Hongpeng +3 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2401.14854
openalex publication_date 2024/01/26 · openalex created_date 2024/01/30 · openalex updated_date 2026/07/28
In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The method is based on a Bernardi--Raugel-like \boldsymbolH(div)-conforming method proposed first for the Stokes flows in [Li and Rui, IMA J. Numer. Anal. 42 (2022) 3711--3734].Therein the lowest-order \boldsymbolH(div)-conforming Raviart--Thomas space (\boldsymbolRT0) was added to the classical conforming \boldsymbolP1× P0 pair to meet the inf-sup condition, while preserving the divergence constraint and some important features of conforming methods. Due to the inf-sup stability of the \boldsymbolP1⊕ \boldsymbolRT0× P0 pair, a locking-free elasticity discretization with respect to the Lamé constant λ can be naturally obtained. Moreover, our scheme is gradient-robust for the pure and homogeneous displacement boundary problem, that is, the discrete \boldsymbolH1-norm of the displacement is O(λ-1) when the external body force is a gradient field. We also consider the mixed displacement and stress boundary problem, whose \boldsymbolP1⊕ \boldsymbolRT0 discretization should be carefully designed due to a consistency error arising from the \boldsymbolRT0 part. We propose both symmetric and nonsymmetric schemes to approximate the mixed boundary case. The optimal error estimates are derived for the energy norm and/or \boldsymbolL2-norm. Numerical experiments demonstrate the accuracy and robustness of our schemes.