Pointwise Constraint
To add a Pointwise Constraint node on the domain, boundary, edge, or point level in any physics interface, click the Show More Options button () and select Equation-Based Contributions in the Show More Options dialog box. 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.
From the Constraint method list, choose Elemental (the default) or Nodal:
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Choose Elemental to make the software assemble the constraint on each node in each element; that is, there are usually several constraints at the same global coordinates because elements in the computational mesh overlap at nodes.
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Choose Nodal to make the software assemble a single constraint for each global node point. The nodal constraint method provides an averaging of the constraints from adjacent elements, which can be beneficial when the constraint has discontinuities between mesh elements (for example, due to discontinuities of the boundary normal). Another case where nodal constraints can be useful is in boundary conditions involving a coupling operator (such as continuity or periodic conditions). With elemental constraints, locking effects can sometimes occur because the coupling operator might map to slightly different points in the source boundary when it is applied to the same node point in different mesh elements.
 
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About Explicit Constraint Reaction Terms
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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 Multiphysics software computes derivatives of Lagrange multipliers and in general does not make any difference at all.
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Working with Geometric Entities
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Settings for the Discretization Sections