What is the difference between a strong and weak solution?

The main difference between weak and strong solutions is indeed that for strong solutions we are given a Brownian motion on a given probability space whereas for weak solutions we are free to choose the Brownian motion and the probability space.

What is the difference between weak form and strong 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 meant by weak formulation?

In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain “test vectors” or “test functions”. …

What is a weak solution in chemistry?

The words we use to describe solutions of acids and bases fall into this category of easily mixed-up definitions. We use the term strong to refer to acids that ionize completely in water, and weak for those acids that are only partially ionized (see Chapter 8 for more information on why).

What is the difference between strong and weak acids?

Strong and weak acids Strong acids dissociate fully in water to produce the maximum number of H + ions. Weak acids, such as ethanoic acid (CH 3COOH), do not fully dissociate.

What is strong solution and weak solution in FEM?

Strong form is the conventional differential equation. 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.

What is the meaning of weak formulation Mcq?

What is the meaning of weak formulation? Solutions obtained are incorrect. The differentiability requirement on primary variable is decreased. The differentiability requirement on primary variable is increased. No Boundary conditions have to be satisfied.

Why is weak form called weak?

On the other hand a weak form states the conditions that the solution must satisfy in an integral sense. The governing equation is combined with the natural boundary conditions in an integral form. The order of derivatives are reduced to (n) and hence “weak” form. the resulted equation is called the weak form.

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.

What do you mean by strong and weak acid?

Strong acids are those that are completely ionized in body fluids, and weak acids are those that are incompletely ionized in body fluids.

What is the difference between strong formulation and weak formulation?

So differentiability of the approximated solution is relaxed. This is called weak formulation where less order assumed solution gives solution of the higher order differential equation. If the order of the assumed solution required to be same as that of differential equation then it is called strong formulation.

What is a weak solution to an equation?

From Wikipedia, the free encyclopedia In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense.

What is the difference between a strong form and a weak form?

A strong form of the governing equations along with boundary conditions states the conditions at every point over a domain that a solution must satisfy. On the other hand a weak form states the conditions that the solution must satisfy in an integral sense. A weak form does not imply “inaccuracy” or “inferiority”.

When is an integrable function a weak solution?

In summary, if the original (strong) problem was to find a | α |-times differentiable function u defined on the open set W such that (a so-called strong solution ), then an integrable function u would be said to be a weak solution if with compact support in W . The notion of weak solution based on distributions is sometimes inadequate.