Biquadric finite element method for parabolic integro-differential equations

Biquadric finite element approximation is established for parabolic integro-differential equations. Based on high accuracy analysis of the element, the superclose property is derived for semi-discrete scheme. Moreover, optimal error estimate is obtained by the interpolation technique instead of the Ritz-Volterra projection which is necessary for classical error estimates of finite element method. Finally, optimal error estimate is deduced for backward Euler discrete scheme.