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Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
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posted on 2023-06-08, 05:17 authored by Erik Burman, Miguel A FernándezThis paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible Navier-Stokes equations. Incompressibility and convective effects are both stabilized, adding an interior penalty term giving $L^2$-control of the jump of the gradient of the approximate solution over the internal faces. Using continuous equal-order finite elements for both velocities and pressures, in a space semi-discretized formulation, we prove convergence of the approximate solution. The error estimates hold irrespective of the Reynolds number, and hence also for the incompressible Euler equations, provided the exact solution is smooth.
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Publication status
- Published
Journal
Numerische MathematikISSN
0029-599XPublisher
Springer VerlagExternal DOI
Issue
1Volume
107Page range
39-77Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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