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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
63/2009

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

Mohammad Izadi Khaleghabadi

Abstract

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.

Received:
Oct 27, 2009
Published:
Nov 3, 2009
MSC Codes:
65N12, 65N15, 65N30, 76N10
Keywords:
a posteriori error estimates, Coupling equations, Dual problem, finite element methods

Related publications

inJournal
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