About Weak Form Modeling
Do not be misled by the term “weak”; the weak form is very powerful and flexible. The term weak form is borrowed  from mathematics, but in this context it has a slightly different meaning; this implementation incorporates capabilities in addition to those defined in the mathematical weak form. Moreover, knowledge of the mathematical weak form is not a prerequisite to using the COMSOL Multiphysics implementation.
The distinguishing characteristics of the weak form in COMSOL Multiphysics are that it makes it possible to:
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Enter certain equations that can be derived from an energy principle in a very compact and convenient form. Such equations, for example, arise in structural mechanics.
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Add and modify nonstandard constraints, such as various contact and friction models.
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Build models with extra equations on boundaries, edges, and points.
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Use the test operator to conveniently work with problems in variational calculus and parametric optimization. For more information about the test operator and other operators, see Operators, Functions, and Constants.
All physics interfaces are implemented as weak form equations, which you can study and modify in the Equation View nodes. COMSOL Multiphysics also converts all equation-based models specified in The Coefficient Form PDE Interfaces and The General Form PDE Interfaces to the weak form before solving.
In addition, it is possible in COMSOL Multiphysics to add extra weak form contributions and auxiliary variables to any physics interface in the model.
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Physics Nodes — Equation Section and Equation View
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About Auxiliary Equation-Based Nodes
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The Weak Form PDE Interfaces and Weak Form PDE