Nonconforming rotated Q 1 element on non-tensor product anisotropic meshes

Abstract

In this paper, we consider the nonconforming rotated Q 1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes, we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.

Optimal Order Error Estimates of a Modified Nonconforming Rotated Q1 IFEM for Interface Problems

“…And a remark is given to explain that the original rotated Q 1 -element proposed in [25] cannot be used for this IFEM, although this element has some advantages over other elements for anisotropic noninterior meshes (cf. [26]). We should point out that the convergence order in the energy norm is half order higher than that in [15] and in which the L 2 -norm was not mentioned.…”