论文标题
压力强大的混合方法几乎不可压缩弹性
Pressure robust mixed methods for nearly incompressible elasticity
论文作者
论文摘要
在过去的几年中，已经开发了不可压缩液体离散的压力鲁棒方法。这些方法允许使用标准有限元来解决问题的解决方案，同时在流体速度的近似误差或不可压缩固体的位移中同时消除了伪压的影响。为此，重建运算符被利用映射到无分歧的功能分散差异功能。这项工作表明，Linke（2014）对Stokes方程提出的修改也产生了梯度鲁棒方法，用于几乎不可压缩的弹性材料，而无需诉诸于FU，Lehrenfeld，Linke，Linke，Streckenbach（2021）中提出的不连续的有限元方法（2021）。
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).
