连续与离散的inf- sup条件用于变形连续体的表面不可压缩性
Continuous and discrete inf-sup conditions for surface incompressibility of a deformable continuum
AI总结：
本文研究了变形连续体表面不可压缩性约束下的inf- sup条件，证明了其稳定性并结合体积守恒条件，为稳定化有限元方法的收敛性提供理论支持。
摘要：
表面不可压缩性，也称为不可伸长性，对封闭变形材料表面的速度施加零散度约束。在该约束下机械问题的适定性依赖于inf- sup或稳定性条件，本文提供了基本证明。结果还显示，与体积守恒约束（等体积性）结合时也成立。这些连续结果随后用于证明一种修改的离散inf- sup条件，这对于稳定化有限元方法的收敛性至关重要。
英文摘要：
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an inf-sup or stability condition for which an elementary proof is provided. The result is also shown to hold in combination with the additional constraint of preserving the enclosed volume, or isochoricity. These continuous results are then applied to prove a modified discrete inf-sup condition that is crucial for the convergence of stabilized finite element methods.
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