On the div-curl lemma in a Galerkin setting
نویسنده
چکیده
Given a sequence of Galerkin spaces Xh of curl conforming vector fields, we state necessary and sufficient conditions under which it is true that the scalar product uh ·uh of two sequences of vector fields uh, uh ∈ Xh converging weakly in L, converges in the sense of distributions to the right limit, whenever uh is discrete divergence free and curluh is precompact in H−1. The conditions on Xh are related to super-approximation and discrete compactness results for mixed finite elements, and are satisfied for Nédélec’s edge elements. We also provide examples of sequences of discrete divergence free edge element vector fields converging weakly to 0 in L but whose divergence is not precompact in H−1 loc.
منابع مشابه
On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma
We study connections between four different types of results that are concerned with vector-valued functions u : Ω → R of class L(Ω) on a domain Ω ⊂ R: Coercivity results in H(Ω) relying on div and curl, the Helmholtz decomposition, the construction of vector potentials, and the global div-curl lemma. Key-words: Friedrichs inquality, coercivity, div-curl lemma, compensated compactness
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