Finite element grad grad complexes and elasticity complexes on cuboid meshes

02/07/2023

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by   Jun Hu, et al.

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This paper constructs two conforming finite element grad grad and elasticity complexes on the cuboid meshes. For the finite element grad grad complex, an H^2 conforming finite element space, an H(curl; 𝕊) conforming finite element space, an H(div; 𝕋) conforming finite element space and an L^2 finite element space are constructed. Further, a finite element complex with reduced regularity is also constructed, whose degrees of freedom for the three diagonal components are coupled. For the finite element elasticity complex, a vector H^1 conforming space and an H(curlcurl^T; 𝕊) conforming space are constructed. Combining with an existing H(div; 𝕊) ∩H(divdiv; 𝕊) element and H(div; 𝕊) element, respectively, these finite element spaces form two different finite element elasticity complexes. The exactness of all the finite element complexes is proved.