Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a spurious pressure influence in the approximation error of the velocity of the fluid, or the displacement of an incompressible solid. To this end, reconstruction operators are utilized mapping discretely divergence free functions to divergence free functions. This work shows that the modifications proposed for Stokes equation by Linke (2014) also yield gradient robust methods for nearly incompressible elastic materials without the need to resort to discontinuous finite elements methods as proposed in Fu, Lehrenfeld, Linke, Streckenbach (2021).

翻译：在过去几年中,开发了使不压缩液体分解的稳健压强方法。 这些方法允许使用标准限值元素解决问题,同时消除流体速度近似误差产生的虚假压力影响,或挤压固态的移位。 为此,重建操作员对离散的自由功能进行绘图,以区分自由功能。 这项工作表明, Linke (2014) 提议的斯托克斯方程式修改还产生了几乎不压缩的弹性材料的梯度强度方法,而无需采用Fu、 Lehrenfeld、 Linke、 Streeckenbach (2021年)中提议的不连续的有限元素方法。