Weakly enforced boundary conditions for the NURBS-based finite cell method

M. Ruess, Y. Bazilevs, D. Schillinger, N. Zander, E. Rank

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement.

Original languageEnglish (US)
Title of host publicationECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Pages7119-7134
Number of pages16
StatePublished - 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: Sep 10 2012Sep 14 2012

Publication series

NameECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

Other

Other6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
CountryAustria
CityVienna
Period9/10/129/14/12

Keywords

  • Fictitious domain
  • Finite cell method
  • NURBS
  • Weakly enforced boundary conditions

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