Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components with respect to its Alfeld split (which connects the vertices to barycenter), generalizing the Johnson-Mercier two-dimensional element to higher dimensions. Further reductions in the stress space in the three-dimensional case (to 24 degrees of freedom per tetrahedron) are possible when the displacement space is reduced to local rigid displacements. Proofs of optimal error estimates of numerical solutions and improved error estimates via postprocessing and the duality argument are presented.

翻译：本文研究了低阶强对称应力线性弹性问题的混合方法。在每个单纯形上，应力空间基于其Alfeld剖分（将顶点连接到重心）具有分片线性分量，将Johnson-Mercier二维元推广到更高维度。当位移空间简化为局部刚性位移时，三维情形下的应力空间可进一步缩减（每个四面体24个自由度）。文中给出了数值解的最优误差估计证明，以及通过后处理和对偶论证实现的改进误差估计。