Fig. 8

The results of the convergence tests. a–c Estimated numerical error \( E\left( {{{\Delta x} \mathord{\left/ {\vphantom {{\Delta x} \lambda }} \right. \kern-0pt} \lambda }} \right) \) as a function of the element size \( {{\Delta x} \mathord{\left/ {\vphantom {{\Delta x} \lambda }} \right. \kern-0pt} \lambda } \). Red symbols represent cases with CM. Green to blue symbols are for cases with NL with various \( h_{T} \). Black pluses are cases with the SBIEM. d–f The cases with NL normalized by \( \left( {{{\Delta x} \mathord{\left/ {\vphantom {{\Delta x} \lambda }} \right. \kern-0pt} \lambda }} \right)^{2} \). Panels in the left, center, and right columns represent Modes I, II, and III, respectively