Adaptive computations on conforming quadtree meshes

Authors:
A. Tabarraei;N. Sukumar
Affiliations:
Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA 95616, USA;Department of Civil and Environmental Engineering, University of California, One Shields Avenue, Davis, CA 95616, USA
Venue:
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Year:
2005

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Abstract

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.