A C0-continuous method achieves stability in boundary value problems, suggesting robust performance with varying parameters.
A C⁰-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity (SGE) in two dimensions. The SGE is a fourth-order singular perturbation problem with a small size parameter. Our proposed method is robust with respect to both the size parameter and the Lamé constant. The stability condition of the VEMs is derived by establishing Korn-type inequalities and inverse inequalities. Some crucial commutative relations for locking-free analysis as in elastic problems are derived. The sharp and uniform error estimates with respect to both the microscopic parameter and the Lamé coefficient are achieved in the lowest-order case, which is also verified by numerical results.
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Huang et al. (2025) studied this question.
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