General Concept
Let be a Banach space. We want to find the solution of the equation
- ,
where and, with being the dual of .
Calculus of variations tells us that this is equivalent to finding such that for all holds:
- .
Here, we call a test vector or test function.
We bring this into the generic form of a weak formulation, namely, find such that
by defining the bilinear form
Since this is very abstract, let us follow this by some examples.
Read more about this topic: Weak Formulation
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