TY - JOUR
T1 - Generalized Gaffney inequality and discrete compactness for discrete differential forms
AU - He, Juncai
AU - Hu, Kaibo
AU - Xu, Jinchao
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on s-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have been established for edge elements with weakly imposed divergence-free conditions and used in the analysis of nonlinear and eigenvalue problems. In this paper, we generalize these results to discrete differential forms, not necessarily with strongly or weakly imposed constraints. The analysis relies on a new Hodge mapping and its approximation property. As an application, we show Lp estimates for several finite element approximations of the scalar and vector Laplacian problems.
AB - We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on s-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have been established for edge elements with weakly imposed divergence-free conditions and used in the analysis of nonlinear and eigenvalue problems. In this paper, we generalize these results to discrete differential forms, not necessarily with strongly or weakly imposed constraints. The analysis relies on a new Hodge mapping and its approximation property. As an application, we show Lp estimates for several finite element approximations of the scalar and vector Laplacian problems.
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U2 - 10.1007/s00211-019-01076-0
DO - 10.1007/s00211-019-01076-0
M3 - Article
AN - SCOPUS:85074232072
SN - 0029-599X
VL - 143
SP - 781
EP - 795
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 4
ER -