A posteriori error estimates for the coupling equations of scalar conservation laws
In this paper we prove a posteriori L (2)(L (2)) and L (a)(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.
a posteriori error estimates coupling equations finite element methods dual problem