What is weak from why it is called a weak form why weak form is desired in FEM?

Weak form is an alternate representation of the differential equation. The strong form imposes continuity and differentiability requirements on the potential solutions to the equation. The weak form relaxes these requirements on solutions to a certain extent.

Why do we use weak formulation?

Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations.

What is the weak form of a PDE?

The weak form is a mathematical manipulation to relax the “strong” requirements for the solution of a PDE. Before going further, keep in mind that weak form doesn’t mean that the solution is weak, or the results got by following this approach would deviate from the actual results.

Why it is called a weak form?

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 do you mean by weak form in FEM?

Weak form means, instead of solving a differential equation of the underlying problem, an integral function is solved. The integral function implicitly contains the differential equations, however it’s a lot easier to solve an integral function than to solve a differential function.

What is strong and weak form?

Grammatical words are words that help us construct the sentence but they don’t mean anything: articles, prepositions, conjunctions, auxiliary verbs, etc. That weakened form is called “weak form” as opposed to a “strong form”, which is the full form of the word pronounced with stress.

How do you identify a weak form?

Weak forms are syllable sounds that become unstressed in connected speech and are often then pronounced as a schwa. In the sentence below the first ‘do’ is a weak form and the second is stressed.