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 and analyzed. Error estimates are presented for first-order transport 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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Burman, E., Ern, A. (2006). Continuous Interior Penalty hp-Finite Element Methods for Transport Operators. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_46
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DOI: https://doi.org/10.1007/978-3-540-34288-5_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
Online ISBN: 978-3-540-34288-5
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