Summary
We introduce a new class of nonconforming finite elements suitable for an accurate approximation of convection-dominated effects and of divergence-free functions and hence also well-suited for the numerical solution of the incompressible Navier-Stokes equations.
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References
Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New York
Ciarlet, P.G. (1991): Basic error estimates for elliptic problems. In: Ciarlet, P.G., Lions, J.-L. (eds.): Handbook of numerical analysis. vol. II. Finite element methods. Part I. North-Holland, Amsterdam, pp. 17–351
Crouzeix, M., Raviart, P.-A. (1973): Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I. Rev. Française Automat. Informat. Recherche Opérationelle Sér, Rouge 7(R-3), 33–76
Girault, V., Raviart, P.-A. (1986): Finite element methods for Navier-Stokes equations. Theory and algorithms. Springer, Berlin
John, V., Maubach, J.M., Tobiska, L. (1997): Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems. Numer. Math. 78, 165–188
Knobloch, P. (2000): On Korn’s inequality for nonconforming finite elements. Tech. Mech. 20, 205–214; Errata, ibid. 375
Knobloch, P. (2001): On the inf-sup condition for the P mod1 element. Preprint MATH-KNM-200l/4. Charles University, Prague
Knobloch, P., Tobiska, L. (1999): The P mod1 element: a new nonconforming finite element for convection-diffusion problems. Preprint 99–28. Fakultät für Mathematik, Otto-von-Guericke-Universität, Magdeburg
Temam, R. (1977): Navier-Stokes equations. Theory and numerical analysis. North-Holland, Amsterdam
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Knobloch, P. (2003). New nonconforming finite elements for solving the incompressible Navier-Stokes equations. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_11
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DOI: https://doi.org/10.1007/978-88-470-2089-4_11
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