Two 11-node nonconforming triangular prism elements for 3D elliptic problems
This work provides new finite element discretizations for 3D elliptic problems, but the contribution is incremental as it extends existing element designs to prismatic meshes.
Two 11-node triangular prism elements are introduced for 3D elliptic problems: an H1-nonconforming element for second-order problems achieving second-order convergence in discrete H1-norm, and an H2-nonconforming element for fourth-order problems achieving first-order convergence in discrete H2-norm. Numerical examples verify the theoretical results.
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 $H^1$-nonconforming and works for second order problems, which achieves a second order convergence rate in discrete $H^1$-norm. The other is $H^2$-nonconforming and solves fourth order problems, with a first order convergence rate in discrete $H^2$-norm. Numerical examples verify our theoretical results.