The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the linear elasticity problem which are free from Poisson locking. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient refinement levels on the fine-scale mesh such that the MHM method is well-posed, optimally convergent under local regularity conditions, and locking-free. Two-dimensional numerical tests assess theoretical results.

翻译：多尺度混合-混合（MHM）方法采用多级策略求解具有非均匀系数的边值问题近似解。针对线性弹性问题，我们提出了一系列低阶有限元族，这些单元可避免泊松闭锁现象。该有限元依赖于基于局部纽曼问题在单元面上采用分片多项式插值构建的多尺度基函数对应的面自由度。我们在细尺度网格上建立了充分的加密层级条件，使得MHM方法适定、在局部正则性条件下最优收敛且无闭锁。二维数值算例验证了理论结果。