What is weak constraint in Comsol?

The weak constraint means simply that it is added directly to the weak form (sometimes there is no strong form to express your constraint, or simply it is more practical to write the weak expression directly). The usual way to add such a constraint still solving the problem consists of adding a Lagrange multiplier.

What are weak constraints?

A weak constraint is respected only on average over each Lagrange multiplier shape function, rather than pointwise at mesh nodes. When it is possible to satisfy the constraint everywhere on each mesh element, standard and weak constraints in general lead to the same solution.

What is weak contribution in Comsol?

Weak contributions are, in fact, what the software internally uses to apply the built-in domain and boundary conditions. They provide a flexible and physics-independent way to extend the applicability of the COMSOL Multiphysics® software.

How can we avoid negative concentration in Comsol?

When the concentration reaches zero, the reaction term continues to consume the species, finally resulting in negative concentration. This can be avoided by making sure that your reaction rate is such that when the concentration of the species approaches zero, then so does the species sink.

How do I add weak contributions to Comsol?

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.

What is test function in Comsol?

While the test function, mathematically, is definded as a more-or-less often differentiable hat-function on a given region, it is displayed in most COMSOL models as something like this. rest_of_equation*(test(uTx) + test(u) + test(vty)) or similar.

How does Comsol solve PDE?

To solve the PDEs, COMSOL Multiphysics uses the proven finite element method (FEM). The software runs the finite element analysis together with adaptive meshing and error control using a variety of numerical solvers.

What does negative concentration mean?

What do they mean? A negative concentration value indicates that the sample was analyzed but that the concentration was below the determination limits of the analytical method.

What is the weak form of an equation?

Weak form – an integral expression such as a functional which implicitly contains a differential equations is called a weak form. The strong form states conditions that must be met at every material point, whereas weak form states conditions that must be met only in an average sense.

What is moving mesh in Comsol?

The moving mesh method for the free surface prescribes the displacement of the rectangular bar and keeps track of the displacement of the water surface. We account for gravity in the model by adding a source in the momentum equations.

What is parametric sweep in Comsol?

Instead of manually changing these property values and resolving each time, you can perform a parametric sweep with COMSOL Multiphysics. A parametric sweep allows you to change the parameter values through a specified range.

What is PDE in Comsol?

The Coefficient Form PDE. The Coefficient Form PDE. In COMSOL Multiphysics, you can define a PDE of this type by specifying coefficients for the derivatives of different orders. This results in a coefficient form PDE, which for one dependent variable u reads: (16-2)

What are constraints in COMSOL Multiphysics?

Frequently, constraints are boundary conditions, but sometimes they can be requirements to be satisfied at every point or by an integral of the solution. Several options for boundary conditions and other constraints are built into COMSOL Multiphysics, but from time to time, you may want to add a novel constraint or two.

What are weak contributions in COMSOL?

Today, we will show you how to implement nonstandard constraints using the so-called weak contributions. Weak contributions are, in fact, what the software internally uses to apply the built-in domain and boundary conditions. They provide a flexible and physics-independent way to extend the applicability of the COMSOL Multiphysics® software.

How to view the weak form for COMSOL Multiphysics physics interface?

The weak form for any COMSOL Multiphysics physics interface can be viewed by enabling the Equation View. If we compare ( Eq. 10) with ( Eq.

What is a weak constraint in math?

The weak constraint means simply that it is added directly to the weak form (sometimes there is no strong form to express your constraint, or simply it is more practical to write the weak expression directly). The usual way to add such a constraint still solving the problem consists of adding a Lagrange multiplier.