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

Burman, Erik; Ern, Alexandre

doi:10.1090/S0025-5718-07-01951-5

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

Authors: Erik Burman and Alexandre Ern
Journal: Math. Comp. 76 (2007), 1119-1140
MSC (2000): Primary 65N30, 65N12, 65N15, 65D05, 65N35
DOI: https://doi.org/10.1090/S0025-5718-07-01951-5
Published electronically: January 24, 2007
MathSciNet review: 2299768
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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.

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