Emergent Mind
A primal finite element scheme of the Hodge Laplace problem
(2208.00575)
Published Aug 1, 2022
in
math.NA
and
cs.NA
Abstract
In this paper, a unified family, for any $n\geqslant 2$ and $1\leqslant k\leqslant n-1$, of nonconforming finite element schemes are presented for the primal weak formulation of the $n$-dimensional Hodge-Laplace equation on $H\Lambdak\cap H*_0\Lambdak$ and on the simplicial subdivisions of the domain. The finite element scheme possesses an $\mathcal{O}(h)$-order convergence rate for sufficiently regular data, and an $\mathcal{O}(hs)$-order rate on any $s$-regular domain, $0<s\leqslant 1$, no matter what topology the domain has.
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