Recently, a multi-level hp-version of the finite element method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hp-approximation capabilities. In the original paper, the refinement procedure made use of a-priori knowledge of the solution. However, adaptive procedures can produce discretizations which are more effective than an intuitive choice of element sizes h and polynomial degree distributions p. This is particularly prominent when a-priori knowledge of the solution is only vague or unavailable. The present contribution demonstrates that multi-level hp-adaptive schemes can be efficiently driven by an explicit a-posteriori error estimator. To this end, we adopt the classical residual-based error estimator. The main insight here is that its extension to multi-level hp-FEM is possible by considering the refined-most overlay elements as integration domains. We demonstrate on several two- and three-dimensional examples that exponential convergence rates can be obtained. © 2016, The Author(s).
|Fachzeitschrift||Advanced Modeling and Simulation in Engineering Sciences|
|Publikationsstatus||Veröffentlicht - 2016|
Systematik der Wissenschaftszweige 2012
- 101 Mathematik
- Explicit error estimation
- High-order FEM
D’Angella, D., Zander, N., Kollmannsberger, S., Frischmann, F., Rank, E., Schröder, A., & Reali, A. (2016). Multi-level hp-adaptivity and explicit error estimation. Advanced Modeling and Simulation in Engineering Sciences, 3(1), . https://doi.org/10.1186/s40323-016-0085-5