Superconvergence of Galerkin Solutions for Hammerstein Equations

Abstract

In the present paper, we discuss the superconvergence of the interpolated Galerkin solutions for Hammerstein equations. With the interpolation post-processing for the Galerkin approximation $x_h$, we get a higher order approximation $I_{2h}^{2r-1}x_h$, whose convergence order is the same as that of the iterated Galerkin solution. Such an interpolation post-processing method is much simpler than the iterated method especially for the weak singular kernel case. Some numerical experiments are carried out to demonstrate the effectiveness of the interpolation post-processing method.