# Hexahedral H(div) and H(curl) finite elements*

Richard S. Falk; Paolo Gatto; Peter Monk

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 1, page 115-143
- ISSN: 0764-583X

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topFalk, Richard S., Gatto, Paolo, and Monk, Peter. "Hexahedral H(div) and H(curl) finite elements*." ESAIM: Mathematical Modelling and Numerical Analysis 45.1 (2011): 115-143. <http://eudml.org/doc/197512>.

@article{Falk2011,

abstract = {
We study the approximation properties of some finite element subspaces of
H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This
work extends results previously obtained for quadrilateral H(div;Ω) finite
elements and for quadrilateral scalar finite element spaces. The finite
element spaces we consider are constructed starting from a given finite
dimensional space of vector fields on the reference cube, which is then
transformed to a space of vector fields on a hexahedron using the appropriate
transform (e.g., the Piola transform) associated to a trilinear isomorphism of
the cube onto the hexahedron. After determining what vector fields are needed
on the reference element to insure O(h) approximation in L2(Ω) and
in H(div;Ω) and H(curl;Ω) on the physical element, we study the properties of
the resulting finite element spaces.
},

author = {Falk, Richard S., Gatto, Paolo, Monk, Peter},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Hexahedral finite element; hexahedral finite element spaces; ; Ωmathvariantupright); ; Ωmathvariantupright)},

language = {eng},

month = {1},

number = {1},

pages = {115-143},

publisher = {EDP Sciences},

title = {Hexahedral H(div) and H(curl) finite elements*},

url = {http://eudml.org/doc/197512},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Falk, Richard S.

AU - Gatto, Paolo

AU - Monk, Peter

TI - Hexahedral H(div) and H(curl) finite elements*

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 1

SP - 115

EP - 143

AB -
We study the approximation properties of some finite element subspaces of
H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This
work extends results previously obtained for quadrilateral H(div;Ω) finite
elements and for quadrilateral scalar finite element spaces. The finite
element spaces we consider are constructed starting from a given finite
dimensional space of vector fields on the reference cube, which is then
transformed to a space of vector fields on a hexahedron using the appropriate
transform (e.g., the Piola transform) associated to a trilinear isomorphism of
the cube onto the hexahedron. After determining what vector fields are needed
on the reference element to insure O(h) approximation in L2(Ω) and
in H(div;Ω) and H(curl;Ω) on the physical element, we study the properties of
the resulting finite element spaces.

LA - eng

KW - Hexahedral finite element; hexahedral finite element spaces; ; Ωmathvariantupright); ; Ωmathvariantupright)

UR - http://eudml.org/doc/197512

ER -

## References

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