This paper describes an investigation into the error bounds of Gauss-L
egendre integration for non-singular integrals in three-dimensional bo
undary element analyses. Based on these numerical results, reliable an
d efficient criteria for adaptive integration routines are proposed. B
ecause these criteria are in simple forms, they can be implemented wit
hin boundary element algorithms without difficulty. Numerical examples
have been presented to demonstrate the efficiency and accuracy of the
proposed integration schemes.