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arXiv · 2506.13041

Mixed Finite element method for stress gradient elasticity

Ting Lin·Shudan Tian
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Abstract

This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error estimates for the proposed pairs, achieving unconditional stability for finite elements with higher vertex continuity and conditional stability for Continuous Galerkin-Discontinuous Galerkin (CG-DG) pairs when no interior vertex has edges lying on three or fewer lines. Numerical experiments validate the theoretical results, demonstrating optimal convergence rates.

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Ting Lin, Shudan Tian. 2025-06-16. Mixed Finite element method for stress gradient elasticity. https://arxiv.org/abs/2506.13041

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