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 approxi-mating 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 of the exact error curve. Moreover, a reasonable estimate of the magnitude of the actual error is also predicted. KEY WORDS: residual estimates; singular and hypersingular residuals; error estimates; boundary element method; singular integrals; hypersingular integrals 1