Computer Methods in Applied Mechanics and Engineering
Knot insertion from a blossoming point of view
Computer Aided Geometric Design
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh medal competition
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
ACM SIGGRAPH 2003 Papers
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Dimensions of spline spaces over T-meshes
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Polynomial splines over hierarchical T-meshes
Graphical Models
Approximation power of polynomial splines on T-meshes
Computer Aided Geometric Design
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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.