A Priori And A Posteriori Error Estimations For The 3-D Rotated Q1 Element With Double Set Parameters

In this paper,a cubic rotated Q1 element with double set parameters(DSP)is presented and analyzed.The cubic rotated Q1 element is the generalization of the rectangular rotated Q1 element.This paper proves that the element doesn't satisfy the anisotropic interpolation properties.We change its form and get a DSP nonconforming cubic element.Then we prove the convergence of this DSP nonconforming cubic element for second order elliptic problems under anisotropic meshes and get the optimal error estimate.Some numerical results are presented,which are accord with our theoretical analysis.Besides,by combining the property of DSP rotated Q1 element with the second order elliptic problems,a posteriori error estimate is given in this paper and gives the detail proof of its reliability and validity.