Abstract: In this paper, Galerkin approximations of Second order hyperbolic equation and parabolic equation are studied with the anisotropic modified rotatedQ1-element and anisotropic biquadratic element respectively. By means of integralidentities and boundary estimates techniques, the convergence analysis is presented for hyperbolic equation, and the superclose result is obtained for parabolic equation respectively. At the same time, based on the superclose property and interpolate post-treatment technique, the Superconvergence result is obtained.
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