Anisotropic interpolations with application to nonconforming elements

Authors:
Shaochun Chen;Yongcheng Zhao;Dongyang Shi
Affiliations:
Department of Mathematics, Zhengzhou University, 450052, People's Republic of China;Department of Mathematics, Zhengzhou University, 450052, People's Republic of China;Department of Mathematics, Zhengzhou University, 450052, People's Republic of China
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

The classical finite element approximation theory relies on the regular or nondegenerate condition, i.e. hK/ρK ≤ c, for all element K, where hk and ρK are diameter of K and diameter of the biggest ball contained in K, respectively. But this condition is not only unnecessary for some finite elements, but also difficult to satisfy in some problems. In this paper a simple criteria condition for getting error estimate of interpolation without the above regular condition is presented. It is used to two well-known nonconforming elements--Wilson's and Adini's elements. The error estimates not only for the interpolation error, but also for the consistency or compatibility error of these two elements are obtained without the above regular condition. Some numerical results are given.