Study Of Gradient Error Estimates Of The Triangulation Interpolated Coefficients Finite Element Methods

In this paper, for the nonlinear tern f(u) of semilinear differential equations, we introduces a more economic and efficient method, called as interpolated coeffient finite element method,which requests that f(u_h) is replaced by interpolation I_hf(u_h)in numerical computation.Based on the previous work,for the semilinear boundary value elliptic problem.In this paper,we study the super convergence of triangulation interpolated coefficients finite element method'average gradient on symmetrical center point and obtains rather satisfactory results.The following are the main contents in this paper1.First,the semilinear two-point boundary value elliptic problem is studied.The regionΩis evenly cutted in half by the triangulation and is linearly interpolated. We prove that the average gradient of the interpolated coefficients finite element has the following superconvergence on symmetrical center pointSecond, the error estimate of the interpolated coefficients finite element' the H¹,L² normis deduced;Next, the problem is interpolated again.Four neighboring elements is constituted a bigger triangulation. u_h is interpolated and obtained I₂u_h.The superconvergence of the biquadratic interpolationis shown.Finally,the better properties are shown by acorresponding numerical experiments.2.For semilinear parabolic problem,We prove that the average gradient of the interpolated coefficients finite element has the same superconvergence on symmetrical center point as the elliptic problem; Next, the fulldiscrete form of the parabolic problem is shown.3.The base computational form of the interpolated coefficients finite element for the semilinear hyperbolic problem is simple discusses.