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：开发了一个新的先决条件,用于在两个维度上对三角贝壳线性弹性问题的高度定序定值元素近似值。新的先决条件产生一个条件编号,该条件编号不受美元、网状大小美元和美元/美元/美元之比的限制。由此得出的条件编号对于标准测试问题参数和离散参数的所有值来说,大约为6.0美元。关键是,新的先决条件总成本与适用基于标准域分解先决条件的成本相当。