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 OptionsDetails
  • LineElement is used to represent line mesh elements in ElementMesh.
  • LineElement 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) 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 Lagrange element.
  • Examples

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    Basic Examples  (1)

    Load the package:

    In[1]:=
    Click for copyable input

    Create a mesh with one line element:

    In[2]:=
    Click for copyable input
    Out[2]=

    Scope  (1)

    Generalizations & Extensions  (4)

    Possible Issues  (6)

    See Also

    ToElementMesh  ToBoundaryMesh  ElementMesh  PointElement  TriangleElement  QuadElement  TetrahedronElement  HexahedronElement

    Tutorials