An Application of New Error Estimation Technique to the Boundary Element Method

In this study, we develop a novel estimation technique to obtain the optimal number of elements in the boundary element method (BEM) without having analytical solution. By using the complete Trefftz set as the analytical solution, namely quasi-analytical solution, the new error estimator is presented in the paper. The error curve versus different number of elements can be derived in the proposed techniques by comparing numerical solution with the quasi-analytical solution. By observing the error curve, we can obtain the optimal number of elements in BEM. One numerical example is taken to demonstrate the accuracy and efficiency of the proposed estimation technique.