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A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions

Burman, E; (2012) A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions. SIAM Journal on Numerical Analysis , 50 (4) 1959 - 1981. 10.1137/10081784X. Green open access

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Abstract

In this paper we show that the nonsymmetric version of Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. For nonconforming elements we prove the same result for the symmetric formulation as well. We prove optimal $H^1$-error estimates and $L^2$-error estimates that are suboptimal with half an order in $h$. Both the pure diffusion and the convection--diffusion problems are discussed.

Type: Article
Title: A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/10081784X
Publisher version: http://dx.doi.org/10.1137/10081784X
Language: English
Additional information: © 2012, Society for Industrial and Applied Mathematics
Keywords: finite element methods, weak boundary conditions, convection dominated flow, stabilized methods
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1384701
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