The Weak Contribution node is available in all interfaces and for all geometry levels, including the global level. The node adds an arbitrary contribution to the total system of equations. Its weak form expression may contain the
test() operator acting on any dependent variable in the model and therefore add contributions to any equation.
Enter the weak-form contribution in the Weak expression field. For example,
-ux*test(ux)-uy*test(uy)+1*test(u) is the weak formulation of Poisson’s equation with
u as the dependent variable and 1 as the source term on the right-hand side. To add a time derivative as in the time-dependent coefficient form PDE, add
-ut*test(u) (notice the sign and the syntax
ut for the time derivative of
u).
These settings affect the numerical integration, and you do not normally need to change them. The Use automatic quadrature settings check box is selected by default, meaning that the settings are taken from the main equation in the interface.
The Integration order specifies the desired accuracy of integration during discretization. Polynomials of at most the given integration order are integrated without systematic errors. For smooth constraints, a sufficient integration order is typically twice the order of the shape function. For example, the default integration order for second-order Lagrange elements is 4. The integration order is a positive integer.
The Integrate on frame setting determines which frame to base the integration on:
Spatial,
Material,
Mesh, or
Geometry. The default frame is the one used for the physics interface.
By default, the Multiply by 2πr check box is selected, which is consistent with the implementation in the physics interfaces. This convention defines all fluxes as per unit area and the natural boundary condition per length and full revolution.
) and select Equation-Based Contributions in the Show More Options dialog box. Then, in the Model Builder, right-click the main interface node and, depending on the geometric entity level, select More>Weak Contribution at the domain or boundary level, Edges>Weak Contribution, Points>Weak Contribution, or Global>Weak Contribution.
