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Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations

Burman, E; Ern, A; (2007) Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Mathematics of Computation , 76 (259) pp. 1119-1140. 10.1090/S0025-5718-07-01951-5. Gold open access

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Abstract

A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpolation result, and hp-error estimates for continuous L2-orthogonal projections.

Type: Article
Title: Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations
Open access status: An open access publication
DOI: 10.1090/S0025-5718-07-01951-5
Publisher version: http://dx.doi.org/10.1068/d14080p10.1090/S0025-571...
Language: English
Keywords: continuous interior penalty, hp-finite element method, convection-diffusion, hp-interpolation and projection, hp-inverse trace inequality
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/1384754
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