Robustness of the boundary integral equation method for potential problems

In previous work the authors investigated the fundamental characteristics of the discretization error of the boundary integral equation method (BEM) through a series of systematic numerical experiments in general 3-D potential problems, and showed that the discretization error is smaller than expected when the lowest order of approximation is used for discretizing the unknown function to be solved. In the present work, they analyze the robustness of the BEM and demonstrate that the discretization errors can be estimated self-consistently in practical applications when the boundary surfaces are discretized into curved elements of various geometries. The effect of varying the mesh size on the local accuracy of solutions is demonstrated on the basis of numerical experiments. From these results, it is possible to formulate strategy to estimate discretization error of a numerical solution in most of the practical applications where no exact solution is available