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A uniformly well-conditioned, unfitted Nitsche method for interface problems
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Design Optimization)
Department of Information Technology, Uppsala University, Uppsala.
Department of Information Technology, Uppsala University, Uppsala.
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Design Optimization)ORCID iD: 0000-0003-0473-3263
2013 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 53, no 3, 791-820 p.Article in journal (Refereed) Published
Abstract [en]

A finite element method for elliptic partial differential equations that allows for discontinuities along an interface not aligned with the mesh is presented. The solution on each side of the interface is separately expanded in standard continuous, piecewise-linear functions, and jump conditions at the interface are weakly enforced using a variant of Nitsche’s method. In our method, the solutions on each side of the interface are extended to the entire domain which results in a fixed number of unknowns independent of the location of the interface. A stabilization procedure is included to ensure well-defined extensions. We prove that the method provides optimal convergence order in the energy and the L2 norms and a condition number of the system matrix that is independent of the position of the interface relative to the mesh. Numerical experiments confirm the theoretical results and demonstrate optimal convergence order also for the pointwise errors.

Place, publisher, year, edition, pages
2013. Vol. 53, no 3, 791-820 p.
Keyword [en]
Interface problem; Nitche's method; Interior penalties; Finite element methods
National Category
Computational Mathematics Computer and Information Science
Identifiers
URN: urn:nbn:se:umu:diva-80314DOI: 10.1007/s10543-012-0417-xOAI: oai:DiVA.org:umu-80314DiVA: diva2:648762
Available from: 2013-09-16 Created: 2013-09-16 Last updated: 2017-12-06

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Wadbro, EddieBerggren, Martin
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