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A Nitsche method for elliptic problems on composite surfaces
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 326, 505-525 p.Article in journal (Refereed) Epub ahead of print
Abstract [en]

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection between any two surfaces in the composite surface is either empty, a point, or a curve segment, called an interface curve. Note that several surfaces can intersect along the same interface curve. On the composite surface we consider a broken finite element space which consists of a continuous finite element space at each subsurface without continuity requirements across the interface curves. We derive a Nitsche type formulation in this general setting and by assuming only that a certain inverse inequality and an approximation property hold we can derive stability and error estimates in the case when the geometry is exactly represented. We discuss several different realizations, including so called cut meshes, of the method. Finally, we present numerical examples. 

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 326, 505-525 p.
Keyword [en]
A priori error estimates, Composite surfaces, Laplace–Beltrami operator, Nitsche method, Inverse problems, Partial differential equations, Approximation properties, Beltrami, Composite surface, Continuity requirements, Elliptic partial differential equation, Finite element space, Priori error estimate, Finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-37566DOI: 10.1016/j.cma.2017.08.033Scopus ID: 2-s2.0-85029527302OAI: oai:DiVA.org:hj-37566DiVA: diva2:1147403
Available from: 2017-10-05 Created: 2017-10-05 Last updated: 2017-10-06

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Citation style
  • apa
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