We present an efficient way to implement the Boundary Element Method (BEM) to capture high activity regions in a boundary value problem. In boundary regions where accuracy is critical, like in adaptive surface meshes, the method of choice is Local Defect
Correction (LDC). We formulate the method and demonstrate its applicability and reliability by means of an example. Numerical results show that LDC and BEM together provide accurate solutions with less computational requirements given that BEM systems usually consist of dense matrices.