Abstract
In this paper, we suggest a new technique for the numerical computation of the local residual of nonlinear hyperbolic conservation laws. This techniques relies on a discrete regularization of the numerical data.
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References
O. Friedrich, Weighted Essentially Non-Oscillatory Schemes for the interpolation of Mean Values on Unstructured Grids. J. Comp. Phys. 144 (1998), pp. 194–212.
I. Thomas and T. Sonar, On a Second Order Residual Estimator for Numerical Schemes for Nonlinear Hyperbolic Conservation Laws. J. Comp. Phys. accepted for publication.
T. Sonar, Strong and weak norm refinement indicators based on the finite element residual for compressible flow computation, Impact of Computing in Science and Engineering, 5 (1993), pp. 111–127.
D. Hempel, Rekonstruktionsverfahren auf unstrukturierten Gittern zur numerischen Simulation von Erhaltungsprinzipien, Dissertation, Universität Hamburg, 1999.
P. houston, J.A. mackenzie, E. Suli, G. Warnecke, A posteriori error analysis for numerical approximations of Friedrichs systems, Num. Math., 82 (1999), pp. 433–470.
C. Johnson, A. Szepessy, Adaptive finite element methods for conservation laws based on a posteriori error estimates, Comm. Pure Appl. Math., 48 (1995), pp. 199–234.
T. Sonar, V. Hannemann, D. Hempel, Dynamic Adaptivity and Residual Control in Unsteady Compressible Flow Computation, Mathematical and Computer Modelling 20 (1994), pp. 201–213.
T. Sonar and E. Suli, A dual graph-norm refinement indicator for finite volume approximations of the Euler equations, Numerische Mathematik, 78 (1998), pp. 619–658.
C. Chanais-Hillairet, Finite volume schemes for a nonlinear hyperbolic equation. convergence towards the entropy solution and error estimate., tech. rep., UMPA, E.N.S. Lyon, 1997.
D. KRÖner, M. Ohlberger, A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions, Math. Comp. 69(2000), pp. 25–39.
P. Woodward, P. Colella, The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks, J. Comp. Phys. 54, (1984), pp. 115–173
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Sonar, T., Thomas, I. (2001). On a Second Order Residual Estimator for Nonlinear Conservation Laws. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_40
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_40
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
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