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

作　　者：Qian Zhang Min Zhang Zhimin Zhang 

机构地区：[1]Department of Mathematical Sciences,Michigan Technological University,Houghton,MI 49931,USA [2]Beijing Computational Science Research Center,Beijing,China [3]Department of Mathematics,Wayne State University,Detroit,MI 48202,USA

出　　处：《Communications in Computational Physics》2023年第10期1332-1360,共29页计算物理通讯（英文）

基　　金：supported in part by the National Natural Science Foundation of China grants NSFC 12131005 and NSAF U2230402.

摘　　要：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 ν.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[H^(1)(Ω)]^(3),can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.

关 键 词：Nonconforming elements -curlΔcurl problem Brinkman problem finite element de Rham complex Stokes complex 

分 类 号：O17[理学—数学]