FEMDocumentation`
FEMDocumentation`

# HexahedronElement

HexahedronElement[{{i11,,i18},,{in1,,in8}}]

represents n linear hexahedron elements ek with incidents {ik1,ik8}.

HexahedronElement[{{i11,,i120},,{in1,,in20}}]

represents n quadratic hexahedron elements ek with incidents {ik1,,ik20}.

HexahedronElement[{e1,,en},{m1,,mn}]

represents n hexahedron elements ek and n integer markers mk.

# Details

• HexahedronElement is used to represent hexahedron mesh elements in ElementMesh.
• HexahedronElement can be used as an input to ToElementMesh or ToBoundaryMesh.
• Incidents ikj are integers that index an array of spatial coordinates. The coordinates referenced by ek={ik1,} are the nodes of the k triangle.
• The first three incidents ik1 until ik8 are always vertices.
• For quadratic triangle elements, the next 12 incidents are mid-side nodes of possibly curved edges.
• Linear elements are order 1 elements and quadratic elements are order 2 elements.
• In HexahedronElement[{e1,,en}], all elements ek need to be of the same order.
• The hexahedra in HexahedronElement[{e1,,en}] will share common nodes, edges, and faces, but cannot intersect with each other or with themselves.
• The nodes for a linear and a quadratic hexahedron are shown:
• For a HexahedronElement, the incidents on the faces must be counterclockwise when viewed from inside the element. An element {i1,,i8} has face incidents {i1,i2,i3,i4}, {i8,i7,i6,i5}, {i1,i5,i6,i2}, {i2,i6,i7,i3}, {i3,i7,i8,i4}, and {i4,i8,i5,i1} for the six faces.
• The hexahedron element is known in the finite element method as a Lagrange element.

# Examples

open allclose all

## Basic Examples(1)

Load the package:

 In[1]:=

Create a mesh with one quad element:

 In[2]:=
 Out[2]=