FEMDocumentation`
FEMDocumentation`

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

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Basic Examples  (1)

Load the package:

Create a mesh with one line element:

Scope  (1)

Create a boundary mesh with line elements:

Visualize the wireframe:

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:

Possible Issues  (6)

The incidents must be of the appropriate length:

The incidents 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:

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_2022_lineelement, author="Wolfram Research", title="{LineElement}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}", note=[Accessed: 05-October-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_lineelement, organization={Wolfram Research}, title={LineElement}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/LineElement.html}, note=[Accessed: 05-October-2022 ]}