论文标题
一种抽象稳定方法，应用于非线性不可压缩弹性
An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
论文作者
论文摘要
在本文中，我们提出和分析一个抽象稳定的混合有限元框架，该元素可以应用于非线性不可压缩的弹性问题。在抽象稳定的框架中，我们证明，满足离散INF-SUP条件的任何混合有限元方法都可以修改，以便只要混合连续问题稳定，它是稳定且最佳收敛的。此外，我们将抽象稳定的框架应用于非线性不可压缩的弹性问题，并提出数值实验以验证理论结果。
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element method that satisfies the discrete inf-sup condition can be modified so that it is stable and optimal convergent as long as the mixed continuous problem is stable. Furthermore, we apply the abstract stabilized framework to nonlinear incompressible elasticity problems and present numerical experiments to verify the theoretical results.
