Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method |
| |
| Authors: | Erik Burman Peter Hansbo |
| |
| Affiliation: | 1. Department of Mathematics, University of Sussex, Falmer, BN1 9RF, UK;2. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-41296 Göteborg, Sweden;1. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;2. Institute for Computational Mechanics, Technical University of Munich, Boltzmannstraße 15, 85747 Garching, Germany;1. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK;2. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;3. Department of Mechanical Engineering, Jönköping University, SE-551 11 Jönköping, Sweden;1. Department of Mechanical Engineering, Jönköping University, SE-551 11 Jönköping, Sweden;2. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;3. Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden;1. Department of Mathematics, University College London, London, UK-WC1E 6BT, United Kingdom;2. Department of Mechanical Engineering, Jönköping University, SE-55111 Jönköping, Sweden;3. Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran;2. Department of Industrial Engineering, Isfahan University of Technology, Isfahan, Iran;3. Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik (M-10), Technische Universität Hamburg-Harburg, Hamburg, Germany;4. Lehrstuhl für Computation in Engineering, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München, München, Germany |
| |
| Abstract: | We propose a fictitious domain method where the mesh is cut by the boundary. The primal solution is computed only up to the boundary; the solution itself is defined also by nodes outside the domain, but the weak finite element form only involves those parts of the elements that are located inside the domain. The multipliers are defined as being element-wise constant on the whole (including the extension) of the cut elements in the mesh defining the primal variable. Inf–sup stability is obtained by penalizing the jump of the multiplier over element faces. We consider the case of a polygonal domain with possibly curved boundaries. The method has optimal convergence properties. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
