Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes

Cosmin Anitescu, Md Naim Hossain, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)


An adaptive higher-order method based on a generalization of polynomial/rational splines over hierarchical T-meshes (PHT/RHT-splines) is introduced. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial simulations have rough solutions. This can be caused, for example, by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis is less suitable for resolving the singularities that appear, as refinement propagates throughout the computational domain. Hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities, by adding more degrees of freedom only where they are necessary to improve the approximation. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this work. The estimator produces a “recovered solution” which is a more accurate approximation than the computed numerical solution. Several 2D and 3D numerical investigations with PHT-splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost.

Original languageEnglish
Pages (from-to)638-662
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2018 Jan 1
Externally publishedYes

Bibliographical note

Funding Information:
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme ( FP7/2007–2013 )/ ERC grant agreement 615132 and from the People Programme (Marie Curie Actions) under Research Executive Agency grant agreement 289361 .

Publisher Copyright:
© 2017 Elsevier B.V.


  • Error estimation
  • Hierarchical splines
  • Isogeometric analysis
  • Linear elasticity
  • Superconvergent patch recovery

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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