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Galerkin method is used heavily in finite element method, which can conveniently convert continuous problems to discrete ones. Particularly, Galerkin method can be used to prove uniqueness existence of solutions of some kinds of partial differential equations. But I can only find the detail of this for parabolic equations. I wonder how to have it applied to hyperbolic equations. Can anyone give some references? Thank you.

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    But I think Stig Larsson and Vidar Thomee's book _$P$artial Di$f$$f$erential Equations with Numerical Methods_ does address FEM for hyperbolic equations, so presumably something similar to what you are looking for is in there.2011-06-26

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