What is the weak form of a PDE?
A weak form is defined to be a weighted integral statement of a differential equation in which the differentiation is transferred from the dependent variable to the weight function such that all natural boundary conditions of the problem are also included in the integral statement.
What are examples of strong and weak forms?
Pronouns
| orthography | strong form(s) | weak form(s) |
|---|---|---|
| his | hɪz | ɪz |
| him | hɪm | ɪm |
| her | hɜː | hə, ə, ɜː |
| you | juː | jʊ, jə |
Which is the weak form of the differential equation?
A weak form of the differential equations is equivalent to the governing equation and boundary conditions, i.e. the strong form. In many disciplines, the weak form has specific
Which is the main idea of the weak form?
The main idea of the weak form is to turn the differential equation into an integral equation, so as to lessen the burden on the numerical algorithm in evaluating derivatives. To turn the differential equation (2) into an integral equation, a naive first approach may be to integrate it over the entire domain :
Can a differential equation be turned into an integral equation?
To turn the differential equation (2) into an integral equation, a naive first approach may be to integrate it over the entire domain : This asks that the average value of in the entire domain is zero. Indeed, it seems “too weak” as compared to the original differential equation, which asks that should be zero everywhere in the interval .
How is the weak form used in physics?
About the Weak Form, Briefly For many of the different types of physics simulated with COMSOL Multiphysics, a weak formulation, or weak form, is used behind the scenes to construct the mathematical model.