Adaptive finite element methods for elliptic equations over hierarchical T-meshes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article; Proceedings Paper

Tian, Li¹  Chen, Falai²  Du, Qiang¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

关键词: Numerical PDEs;    Adaptive finite element;    Adaptive PHT-splines;    A posteriori error estimations;    Hierarchical T-meshes;   

DOI  :  10.1016/j.cam.2011.05.016

来源: Elsevier

【 摘 要 】

Isogeometric analysis using NURBS (Non-Uniform Rational B-Splines) as basis functions gives accurate representation of the geometry and the solution but it is not well suited for local refinement. In this paper, we use the polynomial splines over hierarchical T-meshes (PHT-splines) to construct basis functions which not only share the nice smoothness properties as the B-splines, but also allow us to effectively refine meshes locally. We develop a residual-based a posteriori error estimate for the finite element discretization of elliptic equations using PHT-splines basis functions and study their approximation properties. In addition, we conduct numerical experiments to verify the theory and to demonstrate the effectiveness of the error estimate and the high order approximations provided by the numerical solution. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free