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- W2995588377 abstract "Abstract We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The permutations of vertex indices correspond to the symmetry group of the simplex. That symmetry group is represented on simplicial finite element spaces by the pullback action. We determine a natural notion of invariance and sufficient conditions on the dimension and polynomial degree for the existence of invariant bases. We conjecture that these conditions are necessary too. We utilize Djoković and Malzan’s classification of monomial irreducible representations of the symmetric group and show new symmetries of the geometric decomposition and canonical isomorphisms of the finite element spaces. Explicit invariant bases with complex coefficients are constructed in dimensions two and three for different spaces of finite element differential forms." @default.
- W2995588377 created "2019-12-26" @default.
- W2995588377 creator A5054231430 @default.
- W2995588377 date "2023-04-27" @default.
- W2995588377 modified "2023-09-30" @default.
- W2995588377 title "Symmetry and Invariant Bases in Finite Element Exterior Calculus" @default.
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- W2995588377 doi "https://doi.org/10.1007/s10208-023-09609-8" @default.
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