A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the degree $p$, the mesh-size $h$ and the ratio $\lambda/\mu$. The resulting condition number is reduced to roughly $6.0$ for all values of the parameters and discretization parameters on standard test problems. Crucially, the overall cost of the new preconditioner is comparable to the cost of applying standard domain decomposition based preconditioners.

翻译：本文针对二维三角网格上线性弹性问题的高阶有限元逼近，提出了一种新的预条件子。该预条件子使得条件数有界，且与次数 $p$、网格尺寸 $h$ 以及比值 $\lambda/\mu$ 无关。在标准测试问题中，对所有参数及离散参数，所得条件数均降至约 $6.0$。关键的是，新预条件子的总体成本与基于标准区域分解的预条件子相当。