Example 1: Linear System of Equations
Now, let and a linear mapping. Then, the weak formulation of the equation
involves finding such that for all the following equation holds:
where denotes an inner product.
Since is a linear mapping, it is sufficient to test with basis vectors, and we get
Actually, expanding, we obtain the matrix form of the equation
where and .
The bilinear form associated to this weak formulation is
Read more about this topic: Weak Formulation
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