The Weak Contribution on Mesh Boundaries node is available on the domain level in all physics interfaces. To add this node, click the Show More Options button () and select Equation-Based Contributions in the Show More Options dialog box. Then right-click the main PDE node and select More>Weak Contribution on Mesh Boundaries at the domain level.

This node is very similar to the Weak Contribution (PDEs and Physics) node on the boundary level, except that it requires a domain selection. Otherwise, the settings are identical. The domain selection is interpreted as all mesh element boundaries (edges in 2D and faces in 3D) in the interior of the selected domains.

Use a Weak Contribution on Mesh Boundaries node to set up boundary conditions between every pair of adjacent mesh elements in its domain selection. To access values in the two adjacent elements, use the up() and down() operators. In practice, this node must be used together with discontinuous shape functions to implement a discontinuous Galerkin method. You can also right-click to add an Auxiliary Dependent Variable subnode.