A primal finite element scheme of the Hodge Laplace problem

08/01/2022

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by   Shuo Zhang, et al.

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In this paper, a unified family, for any n⩾ 2 and 1⩽ k⩽ n-1, of nonconforming finite element schemes are presented for the primal weak formulation of the n-dimensional Hodge-Laplace equation on HΛ^k∩ H^*_0Λ^k and on the simplicial subdivisions of the domain. The finite element scheme possesses an 𝒪(h)-order convergence rate for sufficiently regular data, and an 𝒪(h^s)-order rate on any s-regular domain, 0<s⩽ 1, no matter what topology the domain has.