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What are boundary or initial requirements? probably for most physical or technical problems they are set as values of u on certain surfaces. So You have to provide 1-st order equations in order to solve it.

There You have nearly exact remark about this fact http://en.wikipedia.org/wiki/Finite_element_method#Technical_discussion

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What are boundary or initial requirements? probably for most physical or technical problems they are set as values of u on certain surfaces. So You have to provide 1-st order equations in order to solve it.