

Preprint 63/2009
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