FEMDocumentation`
FEMDocumentation`

TetrahedronElement

TetrahedronElement[{{i11,i12,i13,i14},,{in1,in2,in3,in4}}]

represents n linear tetrahedron elements ek with incidents {ik1,ik2,ik3,ik4}.

TetrahedronElement[{{i11,,i110},,{in1,,in10}}]

represents n quadratic tetrahedron elements ek with incidents {ik1,,ik10}.

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

represents n tetrahedron elements ek and n integer markers mk.

Details

• TetrahedronElement is used to represent tetrahedron mesh elements in ElementMesh.
• TetrahedronElement 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 tetrahedron.
• The first four incidents ik1, ik2, ik3, and ik4 are always vertices.
• For quadratic tetrahedron elements, the next six incidents are mid-side nodes of possibly curved edges.
• Linear elements are order 1 elements and quadratic elements are order 2 elements.
• In TetrahedronElement[{e1,,en}], all elements ek need to be of the same order.
• The tetrahedra in TetrahedronElement[{e1,,en}] will share common nodes, edges, and faces but cannot intersect with each other, or for second-order tetrahedra, with themselves.
• The nodes for a linear and a quadratic tetrahedra are shown:
• For a TetrahedronElement, the face incidents opposite a vertex ij must be counterclockwise. An element {i1,i2,i3,i4} has the face incidents {i4,i3,i2}, {i4,i1,i3}, {i4,i2,i1}, and {i1,i2,i3} for the four faces.
• The tetrahedron element is knnown in the finite element method as a Lagrange element.

Examples

open allclose all

Basic Examples(1)

 In[1]:=

Create a mesh with one quad element:

 In[2]:=
 Out[2]=