Pointwise Constraint

To add a Pointwise Constraint node on the domain, boundary, edge, or point level, click the Show button () and select Advanced Physics Options. Then, depending on the geometric entity level, select More>Pointwise Constraint at the domain or boundary level, Edges>Pointwise Constraint, or Points>Pointwise Constraint from the context menu. There is no global pointwise constraint option.

This node adds standard pointwise constraints, similar to the ones used by boundary conditions of a constraint type in the physics interfaces.

Use Pointwise Constraint nodes to add extra constraints to a physics interface and to assume complete control over constraint reaction terms and points of application.

Pointwise Constraint

These settings are similar to those for the Weak Constraint, but pointwise constraints do not need explicit, named Lagrange multipliers. Instead, implicit Lagrange multipliers are eliminated by the solvers, together with the degrees of freedom being constrained.

Select an option from the Apply reaction terms on list: All physics (symmetric) (the default) or User defined. For either option, enter a Constraint expression, which COMSOL Multiphysics constrains to 0. For example, entering 2-(u+v) constrains u+v to the value 2.

For User defined, enter also a Constraint force expression. Note that the constraint force expression must use the test() or var() operator. For example, write test(-u) to enforce the constraint by modifying only the u equation with reaction terms.

• About Explicit Constraint Reaction Terms • Constraint Reaction Terms

See Coefficient Form PDE for all the settings and Compact and Standard Notations for Classical PDEs for the equations that the Classical PDE interface solve.

Discretization

Select a Shape function type (finite element types): Lagrange (the default), Hermite, Discontinuous Lagrange, Nodal discontinuous Lagrange, Discontinuous scalar density, Bubble, or Gauss point data.

Select an associated Element order (the order of the shape function for the element). The default is to use Quadratic Lagrange elements.

In most cases, use the same shape function type and order for the pointwise constraint as for the dependent variables being constrained. If dependent variables of different order appear in the constraint expression, select the highest order for the pointwise constraint. Notable exceptions are the Hermite and Argyris shape functions, which should be constrained by Lagrange elements of the corresponding order.

The Frame list is available when there is more than one unique frame in the model. In this case, select Geometry, Mesh, Spatial (the default), or Material from the Frame list. This choice only affects how the COMSOL software computes derivatives of Lagrange multipliers and in general does not make any difference at all.

• Working with Geometric Entities • Settings for the Discretization Sections