Summary: Considering the both effect of boundary approximation and numerical quadrature, a second-order isoparametric element method is given to solve the homogeneous isotropic plane linear elasticity problem in domain \(\Omega\) with curved boundary. By using technically analysis, the optimal error estimate with \(\| \vec{\widetilde{u}} - \vec{u}_h \|_{1, \Omega_h} = O (h^2)\) is obtained, where the function \(\vec{\widetilde{u}}\) is an extension of the true solution \(\vec{u}\) to \(\widetilde{\Omega}\). It yields better accuracy than traditional quadratic finite element method. Finally, two numerical examples are presented, which further illustrate the analytical result and show the scheme is effective.
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