it is a strictly positive-definite matrix, so that the system always has a unique solution. (For other problems, these nice properties will be lost.)

Note that the stiffness matrix will be different depending on the computational grid used for the domain and what type of finite element is used. For example, the stiffness matrix when piecewise quadratic finite elements are used will have more degrees of freedom than piecewise linear elements.

The stiffness matrix for other problems

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