Hypersingular Residuals - A New Approach For Error Estimation In The Boundary Element Method

This paper presents a new approach for a posteriori 'pointwise' error estimation in the boundary element method. The estimator relies upon evaluation of the residual of hypersingular integral equations, and is therefore intrinsic to the boundary integral equation approach. A methodology is developed for approximating the error on the boundary as well as in the interior of the domain. Extensive computational experiments have been performed for the two-dimensional Laplace equation and the numerical results indicate that the error estimates successfully track the form bf the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also predicted.