Nonconforming Finite Elements for the -curlΔcurl and Brinkman Problems on Cubical Meshes

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Department of Mathematical Sciences


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 viscosity coefficient v. The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 DOFs on each cube, 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 serendipity finite element space and the piecewise polynomial space.

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Communications in Computational Physics