Arbitrary-level hanging nodes for adaptive -FEM approximations in 3D

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• 作者：Pavel Kus^a ; ^b ; ^{pkus@rice.zcu.cz" class="auth_mail} ; Pavel Solin^c ; ^a ; ^{solin@unr.edu" class="auth_mail} ; David Andrs^d ; ^{david.andrs@inl.gov" class="auth_mail}
• 关键词：Finite element method ; Higher-order elements ; Constrained approximation ; Irregular meshes ; Arbitrary-level hanging nodes ; Automatic adaptivity
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：November 2014
• 年：2014
• 卷：270
• 期：Complete
• 页码：121-133
• 全文大小：1201 K

文摘

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hp$hp$-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.