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

Burman, Erik and Ern, Alexandre (2007) Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Mathematics of Computation, 76 (259). pp. 1119-1140. ISSN 0025-5718

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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 $L^2$-orthogonal projections.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 19:20
Last Modified: 04 Apr 2012 08:48
URI: http://sro.sussex.ac.uk/id/eprint/20165
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