FEMDocumentation`
FEMDocumentation`

QuadElement

QuadElement[{{i11,i12,i13,i14},,{in1,in2,in3,in4}}]

represents n linear quad elements ek with incidents {ik1,ik2,ik3,ik4}.

QuadElement[{{i11,,i18},,{in1,,in8}}]

represents n quadratic quad elements ek with incidents {ik1,,ik8}.

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

represents n quad elements ek and n integer markers mk.

Details and OptionsDetails
  • QuadElement is used to represent quad mesh elements in ElementMesh.
  • QuadElement 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) quad.
  • The first four incidents ik1, ik2, ik3, and ik4 are always vertices.
  • For quadratic quad elements, the next four incidents are mid-side nodes of possibly curved edges.
  • Linear elements are order 1 elements and quadratic elements are order 2 elements.
  • In QuadElement[{e1,,en}], all elements ek need to be of the same order.
  • The quads in QuadElement[{e1,,en}] will share common nodes and edges but cannot intersect with each other or with themselves.
  • The nodes for a linear and a quadratic quad are shown:
  • The incidents {i1,i2,i3,i4} must be ordered so that going from the coordinates referenced by i1 to i2 to i3 to i4 is in the counterclockwise direction.
  • Typically, QuadElement is used for two-dimensional regions, but may be embedded in three dimensions, for example, as a part of a boundary mesh.
  • The quad element is known in the finite element method as a Lagrange element.
  • Examples

    open allclose all

    Basic Examples  (1)

    Load the package:

    In[1]:=
    Click for copyable input

    Create a mesh with one quad element:

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

    Scope  (1)

    Generalizations & Extensions  (4)

    Applications  (3)

    Possible Issues  (6)

    See Also

    ToElementMesh  ToBoundaryMesh  ElementMesh  PointElement  LineElement  TriangleElement  TetrahedronElement  HexahedronElement

    Tutorials