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A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces

Burman, E; Hansbo, P; Larson, MG; Massing, A; Zahedi, S; (2020) A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces. Computer Methods in Applied Mechanics and Engineering , 358 , Article 112645. 10.1016/j.cma.2019.112645. Green open access

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Abstract

We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in R d . The cut finite element method is based on using an embedding of the surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the standard piecewise linear continuous elements to a piecewise linear approximation of the surface. The stabilization consists of a standard streamline diffusion stabilization term on the discrete surface and a so called normal gradient stabilization term on the full tetrahedral elements in the active mesh. We prove optimal order a priori error estimates in the standard norm associated with the streamline diffusion method and bounds for the condition number of the resulting stiffness matrix. The condition number is of optimal order for a specific choice of method parameters. Numerical examples supporting our theoretical results are also included.

Type: Article
Title: A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.cma.2019.112645
Publisher version: https://doi.org/10.1016/j.cma.2019.112645
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: cut finite element method, convection–diffusion–reaction, PDEs on surfaces, streamline diffusion, continuous interior penalty
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/10082503
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