Lagrange and Serendipity Shape Functions
In most of the physics interfaces in the Acoustics Module, and specifically in the Thermoviscous Acoustic interfaces, you can choose between two families of shape functions in the Discretization section: Lagrange and serendipity. The current default (except for the Thermoviscous Acoustics, SLNS approximation interface) is to use serendipity shape functions.
When using a structured mesh, it is advantageous to use the serendipity elements as they generate significantly fewer degrees of freedom (DOFs). 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:
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2D: Quadrilateral elements of discretization order higher than 1.
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3D: Hexahedral, prism, and pyramid elements of discretization order higher than 1.
In the COMSOL Multiphysics Reference Manual:
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The Lagrange Element (shlag)
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The Nodal Serendipity Element (shnserp)
When coupling two physics interfaces that have the same DOFs like, for example, displacement, the same type of shape functions should be used in both interfaces to ensure conformity. Since there is no difference between the two families of shape functions in 1D, this is not an issue when connecting edges.