The convection-diffusion Petrov-Galerkin story

The term ‘Petrov–Galerkin method’ is probably due to Ron Mitchell and his collaborators, and he was certainly very active in studying the application of finite-element methods to second-order partial differential equations ‘with significant first derivatives’. Our aim in the present paper is to trace links between such early methods and the more recent discontinuous Galerkin methods—not only the methods but also their analysis. Also as Mitchell, like the author, was initially steeped in finite-difference methods, we shall sometimes use their manipulation in our analysis.

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Original source : http://imajna.oxfordjournals.org/cgi/content/short...