Two robust nonconforming H$^2-$elements for linear strain gradient elasticity
arXiv:1604.0218715 citationsh-index: 22
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Provides robust numerical methods for strain gradient elasticity, a higher-order perturbation of linear elasticity, which is important for modeling size effects in materials.
The paper proposes two nonconforming finite elements for linear strain gradient elasticity, achieving uniform convergence in the energy norm with respect to the perturbation parameter.
We propose two nonconforming finite elements to approximate a boundary value problem arising from strain gradient elasticity, which is a higher-order perturbation of the linearized elastic system. Our elements are H$^2-$nonconforming while H$^1-$conforming. We show both elements converges in the energy norm uniformly with respect to the perturbation parameter.