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In this paper, we consider elliptic boundary value problems withdiscontinuous coefficients and obtain the asymptotic optimal error estimate$\|u-u_k\|_{1,\Omega}\leqslant Ch|\ln h|^{1/2}\|u\|_{2,\Omega_1+\Omega_2}$ fortriangle linear elements.

Estimate of the Convergence Rate of Finite Element Solutions to Elliptic Equations of Second Order with Discontinuous Coefficients