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MiS Preprint

A Posteriori Error Estimates for the Coupling Equations of Scalar Conservation Laws

Mohammad Izadi Khaleghabadi


In this paper we prove a posteriori $L_two(L_two)$ and $L_infty(H^{-1})$ 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 $\delta=0$. 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.

MSC Codes:
65N12, 65N15, 65N30, 76N10
a posteriori error estimates, Coupling equations, Dual problem, finite element methods

Related publications

2009 Journal Open Access
Mohammad Izadi

A posteriori error estimates for the coupling equations of scalar conservation laws

In: BIT : numerical mathematics, 49 (2009) 4, pp. 697-720