Abstract
We propose and analyze a low-order virtual element for linear elasticity problems. It can be seen as an evolution of the Bernardi–Raugel element to general polygonal meshes. Like the Bernardi–Raugel element, the local degrees of freedoms for the new virtual element are the values of two components of v at vertexes and the values of the lowest moment of normal component of v on each edge. The proposed method is well-posed, and optimal error estimates are obtained in the L2 and H1 norms. Moreover, the generic constants in these estimates are shown to be uniform with respect to the Lamé coefficient λ. Numerical tests are provided to illustrate the good performance of the method and confirm our theoretical predictions.
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