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

Mohammad Izadi Khaleghabadi

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Submission date: 27. Oct. 2009
Pages: 23
published in: BIT : numerical mathematics, 49 (2009) 4, p. 697-720 
DOI number (of the published article): 10.1007/s10543-009-0243-y
Bibtex
MSC-Numbers: 65N12, 65N15, 65N30, 76N10
Keywords and phrases: a posteriori error estimates, Coupling equations, Dual problem, finite element methods
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Abstract:
In this paper we prove a posteriori and 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 . 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