A new error estimation technique for solving torsion bar problem with inclusion by using BEM

Abstract

In this paper, the torsion problem is analyzed by boundary element method (BEM). After applying a new error estimation technique in the BEM, we can derive the numerical error of BEM. We extend the research of previous literature by the authors Chen and Chen [1], to the real engineering problem. This paper estimates the discretizing error caused by using BEM for solving the torsion problem with inclusions. The main characteristic of this technique is that the exact solution is not known in prior. In the technique, we need to create an auxiliary problem that the government equation, domain shape, and boundary condition type are the same as the given real problem. Besides, it has an analytical solution that satisfies the governing equation. We can derive the suitable number of elements by solving the auxiliary problem. Subsequently, by using the suitable number of elements in the BEM, we can obtain the appropriate solution for the real problem. Finally, several cases in the literature are given to illustrate the validity of the novel approach applied in the BEM to solve the real problem.