WOLFRAM

Wolfram Language & System Documentation Center

LineElement[{{i11,i12},…,{in1,in2}}]

represents n linear line elements ek with incidents {ik1,ik2}.

LineElement[{{i11,…,i13},…,{in1,…,in3}}]

represents n quadratic line elements ek with incidents {ik1,ik2,ik3}.

LineElement[{e1,…,en},{m1,…,mn}]

represents n line elements ek and n integer markers mk.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Possible Issues  
See Also
Tech Notes
Related Guides
Cite this Page
NDSolve`FEM`
NDSolve`FEM`

LineElement

LineElement[{{i11,i12},…,{in1,in2}}]

represents n linear line elements ek with incidents {ik1,ik2}.

LineElement[{{i11,…,i13},…,{in1,…,in3}}]

represents n quadratic line elements ek with incidents {ik1,ik2,ik3}.

LineElement[{e1,…,en},{m1,…,mn}]

represents n line elements ek and n integer markers mk.

Details and Options

  • LineElement is used to represent line mesh elements in ElementMesh.
  • LineElement can be used as an input to ToElementMesh or ToBoundaryMesh.
  • Incidents ik,j are integers that index an array of spatial coordinates. The coordinates referenced by ek={ik1,…} are the nodes of the k^(th) line.
  • The first two incidents ik1 and ik2 are always vertices.
  • For quadratic line elements, the third incident is the mid-side node.
  • Linear elements are order 1 elements and quadratic elements are order 2 elements.
  • In LineElement[{e1,…,en}], all elements ek need to be of the same order.
  • The lines in LineElement[{e1,…,en}] will share common nodes but cannot intersect with each other.
  • The nodes for a linear and a quadratic line are shown:
  • Typically, LineElement is used for one-dimensional regions, but may be embedded in two dimensions, for example, as a part of a boundary mesh.
  • The line element is known in the finite element method as a Serendipity element.

Examples

open all close all

Basic Examples  (1)

Load the package:

Wolfram Language code: <<NDSolve`FEM`

Create a mesh with one line element:

Wolfram Language code: ToElementMesh["Coordinates" -> {{0}, {1}}, "MeshElements" -> {LineElement[{{1, 2}}]}]

Scope  (1)

Create a boundary mesh with line elements:

Wolfram Language code: bmesh = ToElementMesh["Coordinates" -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}, "MeshElements" -> Automatic, "BoundaryElements" -> {LineElement[{{1, 2}, {2, 3}, {3, 4}, {4, 1}}]}]

Visualize the wireframe:

Wolfram Language code: bmesh["Wireframe"]

Generalizations & Extensions  (4)

The base coordinates of the linear element:

Wolfram Language code: c = MeshElementBaseCoordinates[LineElement, 1]

The base incidents of the linear element:

Wolfram Language code: e = LineElement[{MeshElementBaseIncidents[LineElement, 1]}]

A mesh with a linear unit element:

Wolfram Language code: mesh = ToElementMesh["Coordinates" -> c, "MeshElements" -> {e}]

Visualization of the linear unit element:

Wolfram Language code: Show[mesh["Wireframe"], mesh["Wireframe"["MeshElement" -> "PointElements", "MeshElementStyle" -> Directive[Red, PointSize[0.02]], "MeshElementIDStyle" -> Blue]]]

The base coordinates of the quadratic element:

Wolfram Language code: c = MeshElementBaseCoordinates[LineElement, 2]

The base incidents of the quadratic element:

Wolfram Language code: e = LineElement[{MeshElementBaseIncidents[LineElement, 2]}]
Wolfram Language code: mesh = ToElementMesh["Coordinates" -> c, "MeshElements" -> {e}]
Wolfram Language code: Show[mesh["Wireframe"], mesh["Wireframe"["MeshElement" -> "PointElements", "MeshElementStyle" -> Directive[Red, PointSize[0.02]], "MeshElementIDStyle" -> Blue]]]

The base face incidents of the linear element:

Wolfram Language code: e = MeshElementBaseFaceIncidents[LineElement, 1]

The base face incidents of the quadratic element:

Wolfram Language code: e = MeshElementBaseFaceIncidents[LineElement, 2]

Possible Issues  (6)

The incidents must be of the appropriate length:

Wolfram Language code: LineElement[{{3}, {4}}]

The incidents order cannot be mixed:

Wolfram Language code: LineElement[{{1, 2}, {2, 3, 7}}]

The incidents must be lists of integers:

Wolfram Language code: LineElement[{{a, 2, 6}, {2, 3, 7}}]

The number of markers must match the number of incidents:

Wolfram Language code: LineElement[{{1, 2}, {2, 3}}, {1, 1, 2}]

Markers must be a vector of integers:

Wolfram Language code: LineElement[{{1, 2}, {2, 3}, {3, 4}, {4, 5}}, {1, 1, 2, a}]

When possible, noninteger markers will be converted to integers:

Wolfram Language code: LineElement[{{1, 2}, {2, 3}, {3, 4}, {4, 5}}, {1, 1, 2, 2.}]
Wolfram Research (2014), LineElement, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html.

Text

Wolfram Research (2014), LineElement, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html.

CMS

Wolfram Language. 2014. "LineElement." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html.

APA

Wolfram Language. (2014). LineElement. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html

BibTeX

@misc{reference.wolfram_2026_lineelement, author="Wolfram Research", title="{LineElement}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_lineelement, organization={Wolfram Research}, title={LineElement}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}, note=[Accessed: 13-June-2026]}