Abstract
In this contribution we will give a survey on rigorous a posteriori error estimates and adaptive methods for finite volume approximations of hyperbolic and convection dominated parabolic conservation laws. Scalar problems are considered as well as weakly coupled systems where the coupling is only due to lower order terms. In the context of scalar hyperbolic conservation laws error estimates are obtained for cell centered finite volume schemes and for the staggered Lax—Friedrichs scheme in multi dimensions. In the case of weakly coupled convection dominated parabolic equations we get a posteriori error estimates for a vertex centered finite volume scheme which are uniform in the lower bound of the diffusion. Numerical experiments underline the applicability of the theoretical results in adaptive computations.
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Kröner, D., Küther, M., Ohlberger, M., Rohde, C. (2003). A Posteriori Error Estimates and Adaptive Methods for Hyperbolic and Convection Dominated Parabolic Conservation Laws. In: Kirkilionis, M., Krömker, S., Rannacher, R., Tomi, F. (eds) Trends in Nonlinear Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05281-5_7
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DOI: https://doi.org/10.1007/978-3-662-05281-5_7
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