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


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


represents n tetrahedron elements ek and n integer markers mk.


  • 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^(th) 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.


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Basic Examples  (1)

Load the package:

Create a mesh with one quad element:

Generalizations & Extensions  (4)

The base coordinates of the linear element:

The base incidents of the linear element:

A mesh with a linear unit element:

Visualization of the linear unit element:

The base coordinates of the quadratic element:

The base incidents of the quadratic element:

The base face incidents of the linear element:

The base face incidents of the quadratic element:

Applications  (1)

A linear tetrahedron element mesh with markers:

Visualizing the index of the coordinates at their respective positions:

Create the mesh:

Visualize the mesh with the elements' markers:

Possible Issues  (6)

The incidents must be of the appropriate length:

The incident order cannot be mixed:

The incidents must be lists of integers:

The number of markers must match the number of incidents:

Markers must be a vector of integers:

When possible, noninteger markers will be converted to integers: