Abstract: Previously we introduced the de Rham complex on $\mathbb{R}^3$ as a different way of looking at the grad, curl, div complex that has a number of advantages (in particular, it gives a universal language for talking about these operators that turns out to be coordinate independent and generalizable to any number of dimensions, including two). In this talk we give an example of how many other complexes of interest in applied (and theoretical) mathematics can be constructed from the de Rham complex, by considering the Elasticity Complex. The motivation for this is that finite element methods for the de Rham complex are well understood, and so this provides an approach to developing stable finite element methods in elasticity and other settings.
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