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Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations
journal contribution
posted on 2023-06-07, 22:37 authored by Erik Burman, Alexandre ErnA 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.
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Publication status
- Published
Journal
Mathematics of ComputationISSN
0025-5718External DOI
Issue
259Volume
76Page range
1119-1140Pages
22.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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