Abstract: With singular quadrature rules,a quadrature method for the second-kind boundary integral equations in linear elasticity problems on polygonal domains is proposed.The discrete matrix can be obtained with no Cauchy singular integral.With the collectively compact convergent theory,we establish a convergence theorem of approximation and get multivariate asymptotic expansions of error.Solving the discrete equations with coarse meshed partitions in paralle,high accurary approximations are obtained by the splitting extrapolation.A posterior error is derived.

Key words: linear elasticity problem, singular integral equation, splitting extrapolation, quadrature method, a posteriori error, polygonal region