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Adaptive computations on conforming quadtree meshes
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DOI：10.1016/j.finel.2004.08.002.png)
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摘要
En 中文
In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is computationally attractive for adaptive numerical simulations. Mesh generation and adaptive refinement of quadtree meshes is straight-forward. However, finite elements are non-conforming on quadtree meshes due to level-mismatches between adjacent elements, which results in the presence of so-called hanging nodes. In this study, we use meshfree (natural-neighbor, nn) basis functions on a reference element combined with an affine map to construct conforming approximations on quadtree meshes. Numerical examples are presented to demonstrate the accuracy and performance of the proposed h-adaptive finite element method. (c) 2005 Elsevier B.V. All rights reserved.
Keyword:
barycentric coordinates
Meshfree methods
natural neighbors
Laplace interpolant
quadtree data structure
hanging nodes
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