Can the "delaunayTriangulation" function be used to create quadratic elements?

I believe that the Partial Differential Equation toolbox requires a geometric element mesh. Can I use the "delaunayTriangulation" function to create geometric elements (for example, 6-noded triangles and 10-noded tetrahedra)?

Answer 1

[MathWorks Support Team]

The "delaunay", "triangulation", and "delaunayTriangulation" functions can only generate linear elements (3-noded triangles and 4-noded tetrahedra) and cannot be used to generate quadratic elements. Determining the locations of the linear nodes and interpolating for the midpoints should be the easiest method of obtaining quadratic elements.

Additionally, it should be noted that a quadratic element mesh is not required for the PDE toolbox. Although the default geometric order for mesh objects created with "generateMesh" is quadratic, the name-value pair ( ... 'GeometricOrder', 'linear') can be used to create a mesh with linear elements. Further information can be seen in the documentation linked below:

https://www.mathworks.com/help/pde/ug/pde.pdemodel.generatemesh.html#namevaluepairs