Abstract
The triangular prism elements are often used in finite element method combined with hexahedral elements to dealing with 3D problems. However, the traditional prism elements based on isoparametric transformation are sensitive to the mesh distortion with accuracy loss for some cases. In this paper, we present a 3D triangular prism spline element with 15 nodes (denoted by TPS15) corresponding to 15 interpolation bases. Different from the isoparametric transformation, these interpolation bases are constructed based on the tetrahedral volume coordinates and the B-net method for spline functions. Theoretically, the triangular prism spline element can achieve the second order completeness in the Cartesian coordinates. We test the TPS15 element by some numerical examples, including that mixed with the hexahedral element. Compared with the isoparametric Serendipity elements, the numerical results show that the spline elements have better accuracy in most cases, especially for the distorted meshes.
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