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Abstract: We develop the theory of mixed finite elements in terms of special inversesystems of complexes of differential forms, defined over cellular complexes.Inclusion of cells corresponds to pullback of forms. The theory covers forinstance composite piecewise polynomial finite elements of variable order overpolyhedral grids. Under natural algebraic and metric conditions, interpolatorsand smoothers are constructed, which commute with the exterior derivative andwhose product is uniformly stable in Lebesgue spaces. As a consequence weobtain not only eigenpair approximation for the Hodge-Laplacian in mixed form,but also variants of Sobolev injections and translation estimates adapted tovariational discretizations.



Author: Snorre Harald Christiansen

Source: https://arxiv.org/







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