Two 11-node nonconforming triangular prism elements for 3D elliptic problems

2018/11/19 by Xinchen Zhou, Zhou, Xinchen, Zhaoliang Meng +5
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1811.07507

openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This work introduces two 11-node triangular prism elements for 3D elliptic problems. The degrees of freedom (DoFs) of both elements are at the vertices and face centroids of a prism cell. The first element is H¹-nonconforming and works for second order problems, which achieves a second order convergence rate in discrete H¹-norm. The other is H²-nonconforming and solves fourth order problems, with a first order convergence rate in discrete H²-norm. Numerical examples verify our theoretical results.

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