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2. 14) can be converted into a variational statement by replacing w B E → −δu, w F BC → δu, wGG → δq. 15) Why these choices? The key rule is: work pairing. 4, fields such as ∇ · q and s should be paired with δu in V so that their product, once integrated to build a functional, represents work or energy. Consequently, w B E must be ±δu, and similarly for the other weight functions. The choice of the right sign is not that crucial, since signs can be tweaked to get cancellations on total-variations later.
Also easily purchased on the Internet as used book. 2. A Potpourri of References The following are listed by (first) author’s alphabetic order. M. Becker, The Principles and Applications of Variational Methods, MIT Press, Cambridge, 1964. A reprinted thesis. Focus on least-squares weighted residual methods applied to nuclear fuel problems. 7 Many of the books listed here are out of print. The advent of the Internet has meant that it is easier to surf for used books across the world without moving from your desk.
M. Finlayson, The Methods of Weighted Residuals and Variational Principles, Academic Press, 1972. Poorly written, disorganized and unfocused but contains material not available elsewhere in book form, especially in Chapters 9 and 10. Focus on chemical engineering problems hinders those interested in other applications. Good guide to literature before 1970. Out of print, not easily found as used book. C. A. J. Fletcher, Computational Galerkin Methods, Springer-Verlag, 1984. A good exposition of the applications of Galerkin techniques to certain classes of problems in fluid dynamics.