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: Lagrange and serendipity. The current default is to use Lagrange shape functions. To display the Discretization section, click the Show button () and select Discretization.
When using a structured mesh it may be advantageous to switch to 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 differs 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
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The Nodal Serendipity Element
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.