The boundary element method is a highly efficient algorithm for numerical solution of partial differential equations, which is widely used in solving electromagnetic field problems in micro- and nano-optics. The complex resonance frequency of circular cavity with different numbers of boundary elements is obtained, and its error is discussed. Major error can be regarded as absorption or amplification of electromagnetic waves by microcavity, which is concluded from the analysis of the quality factor. Then refractive index compensation method for fixing the error introduced by discrete process of boundary integral equation is proposed. The accuracy of the boundary element method is improved at least an order of magnitude after the amendment. Moreover, the correction amount obtained by a center frequency is valid, when it is used in a wide range of frequency around the central frequency. Therefore, the refractive index compensation method makes the calculation accurate and the computing speed significantly improved, the time and memory consumption sharply dropped. At the same time, correcting the simulation error from the physical point of view can be extended to other numerical methods.