On the div-curl lemma in a Galerkin setting (Q734132)
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scientific article; zbMATH DE number 5618001
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the div-curl lemma in a Galerkin setting |
scientific article; zbMATH DE number 5618001 |
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On the div-curl lemma in a Galerkin setting (English)
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19 October 2009
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The div-curl lemma guarantees the convergence of the product \(u_h\cdot u_h'\) in the sense of distributions under specific conditions. Here the necessity of the conditions is analyzed. They are related to super-approximation and discrete compactness results for mixed finite elements, and are satisfied for Nédélec's edge elements. Also examples of sequences of discrete divergence free edge element vector fields are provided that converge weakly to 0 in \(L^{2}\) but whose divergence is not precompact in \(H^{-1}_{\text{loc}}\).
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div-curl lemma
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convergence
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Galerkin method
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mixed finite elements
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