Abstract It is well known that for problems approaching incompressible limits, standard finite element approaches suffer from suboptimal convergence due to a phenomenon known as locking. We analyze this phenomenon and present a robust generalized finite element formulation that enables optimal solution convergence. This approach is explored for the two-dimensional incompressible elasticity equations with a variable Poisson’s ratio, as well as the two-dimensional lid-driven cavity Stokes flow problem using a penalty pressure formulation.

中文翻译：

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使用广义有限元方法求解几乎不可压缩的场问题

摘要 众所周知，对于接近不可压缩极限的问题，标准有限元方法由于称为锁定的现象而遭受次优收敛。我们分析了这种现象，并提出了一个强大的广义有限元公式，可以实现最优解收敛。该方法用于具有可变泊松比的二维不可压缩弹性方程，以及使用惩罚压力公式的二维盖驱动腔斯托克斯流问题。