Lagrange and Serendipity Shape Functions
In the Solid Mechanics and Membrane interfaces, you can choose between two families of shape functions:
Lagrange
and
serendipity
. The default is to use serendipity shape functions.
The serendipity elements have the advantage of generating significantly fewer degrees of freedom for structured meshes. The accuracy is in most cases almost as good as for the Lagrange elements. The Lagrange elements are however less sensitive to strong mesh distortions.
The serendipity shape functions differ from the Lagrange shape functions only for the following element shapes:
•
2D: Quadrilateral elements of discretization order higher than 1
•
3D: Hexahedral, prism, and pyramid elements of discretization order higher than 1
In the
COMSOL Multiphysics Reference Manual
:
•
The Lagrange Element (shlag)
•
The Nodal Serendipity Element (shnserp)
When coupling two structural mechanics physics interfaces, the same type of shape functions should be used in both interfaces to ensure conformity in displacement shape functions. Since there is no difference between the two families of shape functions in 1D, this is not an issue when connecting edges.
