A characteristic Galerkin method with adaptive error control for the continuous casting problem Original Research Article

The continuous casting problem is a convection-dominated nonlinearly degenerate diffusion problem. It is discretized implicitly in time via the method of characteristics, and in space via continuous piecewise linear finite elements. A posteriori error estimates are derived for the L1L1 norm of temperature which exhibit a mild explicit dependence on velocity. The analysis is based on special properties of a linear dual problem in non-divergence form with vanishing diffusion and strong advection. Several simulations with realistic physical parameters illustrate the reliability of the estimators and the flexibility of the proposed adaptive method.