Volume 20, pp. 154-163, 2005.

Convergence analysis of the rotated ${\mathcal{Q}}_1$ element on anisotropic rectangular meshes

Shipeng Mao and Shaochun Chen

Abstract

The main aim of this paper is to study the convergence of the well-known nonconforming rotated ${\mathcal{Q}}_1$ element for the second order elliptic problems on anisotropic rectangular meshes, i.e., the meshes considered in our work do not satisfy the regular assumption. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.

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Key words

anisotropic, interpolation error, nonconforming, the rotated ${\mathcal{Q}}_1$ element

AMS subject classifications

65N30, 65N15