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

作者：Tian Li; Chen Falai; Du Qiang^*

来源：Journal of Computational and Applied Mathematics, 2011, 236(5): 878-891.

DOI：10.1016/j.cam.2011.05.016

• Numerical PDEs
• Adaptive finite element
• Adaptive PHT-splines
• A posteriori error estimations
• Hierarchical T-meshes

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.

• 出版日期2011-10-1
• 单位中国科学技术大学