scholarly journals A remark concerning divergence accuracy order for H(div)-conforming finite element flux approximations

2019 ◽  
Vol 77 (7) ◽  
pp. 1864-1872 ◽  
Author(s):  
Philippe R.B. Devloo ◽  
Agnaldo M. Farias ◽  
Sônia M. Gomes
Keyword(s):  
Finite Element ◽  
Accuracy Order ◽  
Conforming Finite Element ◽  
Element Flux

scholarly journals $$H^1$$-conforming finite element cochain complexes and commuting quasi-interpolation operators on Cartesian meshes

CALCOLO ◽  
2021 ◽  
Vol 58 (2) ◽  
Author(s):  
Francesca Bonizzoni ◽  
Guido Kanschat
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Arbitrary Order ◽  
Inner Product ◽  
Cochain Complex ◽  
Exterior Derivative ◽  
Product Construction ◽  
Cartesian Meshes ◽  
Conforming Finite Element ◽  
Interpolation Operators

AbstractA finite element cochain complex on Cartesian meshes of any dimension based on the $$H^1$$ H 1 -inner product is introduced. It yields $$H^1$$ H 1 -conforming finite element spaces with exterior derivatives in $$H^1$$ H 1 . We use a tensor product construction to obtain $$L^2$$ L 2 -stable projectors into these spaces which commute with the exterior derivative. The finite element complex is generalized to a family of arbitrary order.

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