AI 中文总结
该研究针对线性应力梯度弹性问题，开发了基于对称Taylor--Hood元的混合有限元方法，证明了其在二维和三维单纯形网格上的稳定性，结合Nitsche方法构造了一般边界条件下的格式，数值实验验证了理论结果。
AI 中文摘要
我们基于对称Taylor--Hood元，开发了用于线性应力梯度弹性问题的混合有限元方法。我们在二维和三维的单纯形网格上，证明了对称Taylor--Hood对的稳定性，从而解决了Brezzi、Fortin和Marini在1993年留下的稳定性问题。结合Nitsche方法，我们进一步构造了适用于一般边界条件下线性应力问题的有限元格式。数值实验验证了理论结果。
英文摘要
We develop mixed finite element methods for the linear stress-gradient elasticity problem based on symmetric Taylor--Hood elements. We establish the stability of the symmetric Taylor--Hood pair on simplicial meshes in both two and three dimensions, thereby resolving the stability left open by Brezzi, Fortin, and Marini in 1993. Combing the Nitsche's method, we further construct finite element schemes for linear stress problem in general boundary condition. Numerical experiments confirm the theoretical results.
