Abstract
In this paper we prove a posteriori L 2(L 2) and L ∞(H −1) residual based error estimates for a finite element method for the one-dimensional time dependent coupling equations of two scalar conservation laws. The underlying discretization scheme is Characteristic Galerkin method which is the particular variant of the Streamline diffusion finite element method for δ=0. Our estimate contains certain strong stability factors related to the solution of an associated linearized dual problem combined with the Galerkin orthogonality of the finite element method. The stability factor measures the stability properties of the linearized dual problem. We compute the stability factors for some examples by solving the dual problem numerically.
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Communicated by Anders Szepessy.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Izadi, M. A posteriori error estimates for the coupling equations of scalar conservation laws. Bit Numer Math 49, 697–720 (2009). https://doi.org/10.1007/s10543-009-0243-y
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DOI: https://doi.org/10.1007/s10543-009-0243-y