This paper's aim is to modify the sample point error analysis method proposed by Kawaguchi and Kamiya, and to develop an h-adaptive quadratic boundary element mesh refinement procedure to be used in the two-dimensional elastic problem. Two sample points are taken in each element. The extended error indicators are determined at each of the sample points, and the mesh refinement is enforced if the total error of an element is greater than the average. Examples show that, with the same requirement for accuracy, fewer iteration cycles are needed if compared with the previous version of the sample point error analysis. A crack problem is considered by the proposed method and the stress intensity factor at the crack tip is also calculated by the displacement extrapolating method. The results show the versatility of the modified sample point method in the theory of elasticity.
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