Adaptive Numerical Methods for Transport Dominated Processes

by Alfio Quarteroni, Polytechnic of Milan, Cagliari, Italy,

Document Type: Proceeding Paper

Part of: Modelling of Flood Propagation Over Initially Dry Areas


The numerical approximation of processes of transport and diffusion can be very challenging when the diffusion is small compared to the convection. Standard Galerkin methods need to be stabilized in order to eliminate spurious oscillations. We review some techniques that have been proposed in recent years which eliminate numerical oscillations without downgrading the accuracy of the numerical solution.

Subject Headings: Numerical methods | Finite element method | Adaptive systems | Finite difference method | Oscillations | Numerical models | Approximation methods | Fluid mechanics

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