Summary
We present a systematic procedure to correct 5-point linear schemes so that convergence towards the weak entropy solution of hyperbolic scalar conservation laws can be established while high order accuracy is achieved including at critical points. Our method can be described as a modification of TVD schemes which preserves the BV∩L ∞ stability; entropy convergence is achieved by addition of an extra limiting mechanism which preserves accuracy.
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Jacques, C., Frederic, C. (1989). Uniformly Second Order Convergent Schemes for Hyperbolic Conservation Laws Including Leonard’s Approach. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_6
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DOI: https://doi.org/10.1007/978-3-322-87869-4_6
Publisher Name: Vieweg+Teubner Verlag
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Online ISBN: 978-3-322-87869-4
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