TY - JOUR

T1 - Fortin operator and discrete compactness for edge elements

AU - Boffi, Daniele

N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The basic properties of the edge elements are proven in the original papers by Nédélec [22,23]. In the two-dimensional case the edge elements are isomorphic to the face elements (the well-known Raviart-Thomas elements [24]), so that all known results concerning face elements can be easily formulated for edge elements. In three-dimensional domains this is not the case. The aim of the present paper is to show how to construct a Fortin operator which converges uniformly to the identity in the spirit of [5,4]. The construction is given for any order tetrahedral edge elements in general geometries. We relate this result to the well-known commuting diagram property and apply it to improve the error estimate for a mixed problem which involves edge elements. Finally we show that this result can be applied to the analysis of the approximation of the time-harmonic Maxwell's system.

AB - The basic properties of the edge elements are proven in the original papers by Nédélec [22,23]. In the two-dimensional case the edge elements are isomorphic to the face elements (the well-known Raviart-Thomas elements [24]), so that all known results concerning face elements can be easily formulated for edge elements. In three-dimensional domains this is not the case. The aim of the present paper is to show how to construct a Fortin operator which converges uniformly to the identity in the spirit of [5,4]. The construction is given for any order tetrahedral edge elements in general geometries. We relate this result to the well-known commuting diagram property and apply it to improve the error estimate for a mixed problem which involves edge elements. Finally we show that this result can be applied to the analysis of the approximation of the time-harmonic Maxwell's system.

UR - http://link.springer.com/10.1007/s002110000182

UR - http://www.scopus.com/inward/record.url?scp=0034556469&partnerID=8YFLogxK

U2 - 10.1007/s002110000182

DO - 10.1007/s002110000182

M3 - Article

VL - 87

SP - 229

EP - 246

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 2

ER -