2022/06/17 by Qian Zhang, Min Zhang, Zhang, Qian +3
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2206.08493
openalex publication_date 2022/06/17 · openalex created_date 2022/06/22 · openalex updated_date 2026/07/28
We propose two families of nonconforming elements on cubical meshes: one for the -curlΔcurl problem and the other for the Brinkman problem. The element for the -curlΔcurl problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the parameter ν. The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 degrees of freedom, respectively. The two families of elements are subspaces of H(curl;Ω) and H(div;Ω), and they, as nonconforming approximation to H(gradcurl;Ω) and [H1(Ω)]3, can form a discrete Stokes complex together with the Lagrange element and the L2 element.