  In this paper, we present a Galerkin method for Abel-type integral equation
with a general class of kernel. Stability and quasi-optimal convergence
estimates are derived in ractional-order Sobolev norms. The fully-discrete
Galerkin method is defined by employing simple tensor-Gauss quadrature. We
develop a corresponding perturbation analysis which allows to keep the number
of quadrature points small. Numerical experiments have been performed which
illustrate the sharpness of the theoretical estimates and the sensitivity of
the solution with respect to some parameters in the equation.
