Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 358, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2019.112645
Keywords
Cut finite element method; Convection-diffusion-reaction; PDEs on surfaces; Streamline diffusion; Continuous interior penalty
Funding
- Swedish Foundation for Strategic Research Grant [AM13-0029]
- Swedish Research Council [2011-4992, 2013-4708]
- EPSRC, UK [EP/P01576X/1]
- EPSRC [EP/P01576X/1] Funding Source: UKRI
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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. (C) 2019 Elsevier B.V. All rights reserved.
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