Saddle Points and Ritz–Galerkin Approximations
Victor L. Shapiro · SIAM Journal on Mathematical Analysis · 1980
This paper establishes a theorem for Ritz–Galerkin approximations to a unique saddle point of a function defined on a reflexive Banach space. The functional value at the saddle point is given in terms of an infimum and supremum over two closed, possibly infinite dimensional subspaces whose direct sum determines the original Banach space. Also, an application is given to a nonlinear boundary value problem involving the biharmonic operator.