WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home 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 allclose all

Basic Examples  (1)Summary of the most common use cases

Load the package:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-h9vte9

Create a mesh with one line element:

In[2]:=2
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-jmidlk
Out[2]=2

Scope  (1)Survey of the scope of standard use cases

Create a boundary mesh with line elements:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-l4gi0s
Out[1]=1

Visualize the wireframe:

In[2]:=2
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-685ujy
Out[2]=2

Generalizations & Extensions  (4)Generalized and extended use cases

The base coordinates of the linear element:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-bdlhqr
Out[1]=1

The base incidents of the linear element:

In[2]:=2
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-e986sw
Out[2]=2

A mesh with a linear unit element:

In[3]:=3
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-yi7d7y
Out[3]=3

Visualization of the linear unit element:

In[4]:=4
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-gr7kca
Out[4]=4

The base coordinates of the quadratic element:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-xkd20r
Out[1]=1

The base incidents of the quadratic element:

In[2]:=2
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-4b03mm
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-12438n
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-79tbf8
Out[4]=4

The base face incidents of the linear element:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-gf6ti
Out[1]=1

The base face incidents of the quadratic element:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-j7cpks
Out[1]=1

Possible Issues  (6)Common pitfalls and unexpected behavior

The incidents must be of the appropriate length:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-lvcvm4
Out[1]=1

The incidents order cannot be mixed:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-29oxt4
Out[1]=1

The incidents must be lists of integers:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-cm1i73
Out[1]=1

The number of markers must match the number of incidents:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-3ab5ie
Out[1]=1

Markers must be a vector of integers:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-neqwpm
Out[1]=1

When possible, noninteger markers will be converted to integers:

In[1]:=1
✖
https://wolfram.com/xid/0bzj9dx865xbrheo3b77m-yp4gm6
Out[1]=1
Wolfram Research (2014), LineElement, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html.
✖
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.

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_lineelement, author="Wolfram Research", title="{LineElement}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}", note=[Accessed: 01-May-2025 ]}

✖
@misc{reference.wolfram_2025_lineelement, author="Wolfram Research", title="{LineElement}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}", note=[Accessed: 01-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_lineelement, organization={Wolfram Research}, title={LineElement}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}, note=[Accessed: 01-May-2025 ]}

✖
@online{reference.wolfram_2025_lineelement, organization={Wolfram Research}, title={LineElement}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}, note=[Accessed: 01-May-2025 ]}