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- W2145208522 abstract "This paper proves a discrete analogue of the Poincaré lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone operator, p:Ck(K)→Ck+1(K), as the geometric cone of a simplex cannot, in general, be interpreted as a chain in the simplicial complex. The corresponding cocone operator H:Ck(K)→Ck−1(K) can be shown to be a homotopy operator, and this yields the discrete Poincaré lemma. The generalized cone operator is a combinatorial operator that can be constructed for any simplicial complex that can be grown by a process of local augmentation. In particular, regular triangulations and tetrahedralizations of R2 and R3 are presented, for which the discrete Poincaré lemma is globally valid." @default.
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- W2145208522 date "2005-05-01" @default.
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- W2145208522 title "Discrete Poincaré lemma" @default.
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- W2145208522 doi "https://doi.org/10.1016/j.apnum.2004.09.035" @default.
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