NDSolve`FEM`
NDSolve`FEM`

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

represents n quad elements ek and n integer markers mk.

# Details and Options

• QuadElement 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 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 Serendipity element.

# Examples

open allclose all

## Basic Examples(1)

Create a mesh with one quad element:

## Scope(1)

A boundary mesh with quad 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:

## Applications(3)

Linear quad elements in a mesh:

Visualize the mesh with the elements vertices.

Visualize the mesh with the elements' vertices:

A mixed quad and triangle element mesh with markers:

Visualize the mesh with the elements' markers:

## 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:

#### CMS

Wolfram Language. 2014. "QuadElement." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/FEMDocumentation/ref/QuadElement.html.