ON ADAPTIVE FINITE-ELEMENT METHODS FOR FREDHOLM INTEGRAL-EQUATIONS OF THE 2ND KIND

A posteriori and a priori error estimates are derived for a finite element discretization of a Fredholm integral equation of the second kind. A reliable and efficient adaptive algorithm is then designed for a specific computational goal with applications to potential problems. The reliability of the algorithm is guaranteed by the a posteriori error estimate and the efficiency follows from the a priori error estimate, which shows that the a posteriori error bound is sharp.