Uniform Convergence of Variational Methods for Plane Subsonic Flow
M. J. O’Carroll · IMA Journal of Applied Mathematics · 1974
Uniform convergence is proved for certain direct variational methods, assuming the existence of a solution with certain properties. In particular one important property used is that of “subsonicity”. This is then imposed on the approximating functions in order to establish the uniform convergence. This overcomes a crucial assumption made in previous work for Rayleigh–Ritz approximations. further, previous results for bounded subdomains are extented to infinity. The analysis applies mroe generally to plane uniformly elliptic problems when a priori bounds on the first derivatives of the solution are known to exist.