Summary
The effect of reentrant corners is studied for finite element discretizations of viscous flow problems. In the case of low Reynolds numbers, the pollution effect of the corner singularities is localized to a relatively small neighborhood of the irregular points, depending on the geometry of the domain. However, for problems with strong convection one has to expect some downstream pollution. On the basis of an asymptotic expansion of the discretization error, the computational accuracy can be significantly improved by means of extrapolation or related techniques.
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References
Blum, H., Harig. J., Keller, G., Müller, S.: A numerical comparison of approximation and stability properties of low order Stokes elements,Preprint SFB 123, Univ. Heidelberg 1989, to appear
Blum, H., Harig. J., Müller, S.: Extrapolation techniques for finite element approximations of Stokes and Navier-Stokes flow over a backward facing step, in: Finite Approximations in Fluid Mechanics II (Hirschel, E., ed.), Notes on Numerical Fluid Mechanics 25, Vieweg 1989
Blum, H., Lin, Q., Rannacher, R.: Asymptotic error expansion and Richardson extrapolation for linear finite elements, Numer. Math. 49, 11–37 (1986)
Blum, H., Rannacher, R.: On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Meth. Appl. Sci. 2, 556–581 (1980)
Blum, H., Rannacher, R.: Extrapolation techniques for reducing the pollution effect of reentrant corners in the finite element method, Numer. Math. 52, 539–564 (1988)
Brezzi, F.: On the existence, uniqueness, and approximation of saddlepoint problems arising from Lagrange multipliers, RAIRO, Anal. Numer. R2, 129–151 (1974)
Dobrowolski, M.: Numerical approximation of elliptic interface and corner problems, Habilitationsschrift, Univ. Bonn (1981)
Duran, R., Nocchetto, R.H., Wang., J.: Sharp maximum norm error estimates for finite element approximations of the Stokes problem in 2-D,SIAM J. Numer. Anal., to appear
Kondrat’ev, V.A., Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16, 227–313 (1967)
Morgan,K., Periaux, J., Thomasset, F. (eds.) Analysis of laminar flow over a backward facing step, Notes on Numerical Fluid Mechanics 9, Vieweg 1984
Maz’ja, V.G., Plamenevskij, P.A., Coefficients in the asymptotics of the solutions of elliptic boundary value problems, J. Soy. Math. 9, 750–764 (1980)
Schatz, A.H., Wahlbin, L.B.: Interior maximum norm estimates for finite element methods, Math. Comput. 33, 465–492 (1979)
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© 1990 Springer Fachmedien Wiesbaden
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Blum, H. (1990). The Influence of Reentrant Corners in the Numerical Approximation of Viscous Flow Problems. In: Hackbusch, W., Rannacher, R. (eds) Numerical Treatment of the Navier-Stokes Equations. Notes on Numerical Fluid Mechanics (NNFM), vol 30 5. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14004-7_4
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DOI: https://doi.org/10.1007/978-3-663-14004-7_4
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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