LOCAL ERROR ESTIMATES FOR THE GALERKIN METHOD APPLIED TO STRONGLY ELLIPTIC INTEGRAL EQUATIONS ON OPEN CURVES

摘要

Saranen [Math. Comp., 48 (1987), pp. 485-502] proved local estimates in Sobolev norms for the Galerkin method applied to strongly elliptic equations on smooth closed curves in the plane. We extend his results to the case of open curves. Of particular interest are weakly singular and hypersingular integral equations on a slit. An interesting outcome from our result is that we can judge the orders of convergence of the local errors in some norms that de not exist in the global sense. [References: 18]