The Mixture Of Algebraic And Trigonometric Interpolation To Solve The Homogeneous Problems

Composite material are widely used nowadays industry, in the asymptotic extension of small periodic composite materials'solver, we need know the whole second derivatives of the corre-sponding homogeneous problems. It's hard to obtain by use of normal numerical computation. This paper use finite element methods to construct two-dimensional's fifteen parametric elements and thirty-eight parametric elements containing second derivatives as the node parameter by use of polynomial space as well as supplementary trigonometric functions, it can be applied to homoge-neous problems. We also receive the error estimations under the regular conditions. This construc-tion adapt to the computational demand of composite material's asymptotic extension problem, and has higher convergent order than lower order elements.