We establish a general existence result for Galerkin's approximate solutions of abstract semilinear equations and conduct an error analysis. Our results may be regarded as some extension of a precedent work (Schultz 1969). The derivation of our results is, however, different from the discussion in his paper and is essentially based on the convergence theorem of Newton’s method and some techniques for deriving it. Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.
Tadashi Kawanago. "Error Analysis of Galerkin's Method for Semilinear Equations." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/298640