与弹性复形相关的向量值上链/链复形
A Vector-Valued Co-Chain/Chain Complex Associated to the Elasticity Complex
AI总结：
本研究回顾Christiansen的离散弹性复形，利用其空间自由度构造了同构的向量值链/上链复形，定义了代数算子，还构造了从光滑弹性复形到该离散复形的类似de Rham映射。
AI中文摘要：
在本报告中，我们回顾了Christiansen[2011, Num. Math.]提出的使用多项式和分布空间的离散弹性复形。利用这些空间的自由度，我们构造了一个由向量值链和上链组成的复形，该复形与Christiansen的复形同构。新复形的算子是代数的，但利用了单纯复形的几何性质。最后，我们定义了一个类似de Rham映射，将光滑弹性复形映射到该离散复形。
英文摘要：
In this report, we recall Christiansen's [2011, Num. Math.] discrete elasticity complex that uses spaces of polynomials and distributions. Using the degrees of freedom of those spaces, we write a complex using vector-valued chains and co-chains that is isomorphic to Christiansen's complex. The operators of the new complex are algebraic, but use the geometry of the simplicial complex. Finally, we define a de Rham-like map from the smooth elasticity complex to this discrete complex.
