FEMDocumentation`
FEMDocumentation`

# TriangleElement

TriangleElement[{{i11,i12,i13},,{in1,in2,in3}}]

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

TriangleElement[{{i11,,i16},,{in1,,in6}}]

represents n quadratic triangle elements ek with incidents {ik1,,ik6}.

TriangleElement[{e1,,en},{m1,,mn}]

represents n triangle elements ek and n integer markers mk.

# Details

• TriangleElement is used to represent triangle mesh elements in ElementMesh.
• TriangleElement 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 triangle.
• The first three incidents ik1, ik2, and ik3 are always vertices.
• For quadratic triangle elements, the next three incidents are mid-side nodes of possibly curved edges.
• Linear elements are order 1 elements and quadratic elements are order 2 elements.
• In TriangleElement[{e1,,en}], all elements ek need to be of the same order.
• The triangles in TriangleElement[{e1,,en}] will share common nodes and edges but cannot intersect with each other, or for second order triangles, with themselves.
• The nodes for a linear and a quadratic triangle are shown:
• • The incidents {i1,i2,i3} must be ordered so that going from the coordinates referenced by i1 to i2 to i3 is in the counterclockwise direction.
• Typically, TriangleElement is used for two-dimensional regions, but may be embedded in three dimensions, for example, as a part of a boundary mesh.
• The triangle element is known in the finite element method as a Lagrange element.

# Examples

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## Basic Examples(1)

 In:= Create a mesh with one triangle element:

 In:= Out= 