Error estimation and adaptive mesh refinement are important issues in the boundary element method (BEM). A number of researches have been made in the past two decades and some effective algorithms have been proposed [1]. However, comparing to the potential and elasticity problems, relative few work has been done to the fourth order plate bending problems which is also of engineering significance. In this paper, an overview is made to error estimation and adaptivity algorithms in plate bending BEM analysis and emphasis is put on the differences of the algorithms between plate bending and normally the potential and elasticity problems. Then a simple a-posteriori error estimation algorithm is proposed for plate bending BEM and it is further used to conduct an h-type adaptive mesh refinement procedure.In the plate bending BEM analysis, boundary integral equations (BIEs) for normal and tangential slopes are both hyper-singular. Based on recent researches [2-3], the residual of the hyper-singular boundary integral equations (HBIEs) can be used as an a-posteriori error estimation for different kinds of problems, which is especially significant to adaptive scheme in BEM. In the present paper, the regularized hyper-singular plate bending BIEs are first investigated as an indirect calculation method of integrals. Rigid deflection and normal or tangential slope fields are introduced to regularize the singular or hyper-singular BIEs instead of placing the source boundary outside the actual boundary in some regularization methods. Two regularized equations for normal slope and tangential slope, which can greatly improve the accuracy of the numerical solutions in analysis, are obtained. The conventional plate bending BEM analysis and HBIEs are adopted simultaneously to present two solutions, and the measure of the difference of two solutions furnishes a new a-posteriori error indicator. Both Hermitian [4] and Lagrangian elements are used to test the efficiency of the proposed algorithm. Results of the typical numerical examples show that the new error indicator is simple and effective.
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