Spline element methods allowing multiple level hanging nodes

Spline element methods allowing multiple level hanging nodes In this paper, a systematic algorithm of spline element method allowing multiple level hanging nodes on triangular mesh is proposed. The classical smoothness condition of the piecewise polynomials on triangular mesh is generalized to the case of meshes with hanging nodes, and is treated as the linear constraints of the system equations. We then derive a concise formulation for such linear constraints according to the special hierarchical configurations of the hanging nodes. Moreover, an efficient linear equation solver is proposed when applied to solve the elliptic partial differential equations. Numerical examples are illustrated to show the accuracy of the proposed methods, and the comparisons are made between different levels of hanging nodes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

Spline element methods allowing multiple level hanging nodes

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2018.01.013
Publisher site
See Article on Publisher Site

Abstract

In this paper, a systematic algorithm of spline element method allowing multiple level hanging nodes on triangular mesh is proposed. The classical smoothness condition of the piecewise polynomials on triangular mesh is generalized to the case of meshes with hanging nodes, and is treated as the linear constraints of the system equations. We then derive a concise formulation for such linear constraints according to the special hierarchical configurations of the hanging nodes. Moreover, an efficient linear equation solver is proposed when applied to solve the elliptic partial differential equations. Numerical examples are illustrated to show the accuracy of the proposed methods, and the comparisons are made between different levels of hanging nodes.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 1, 2018

References

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