Istituto di Matematica Applicata e Tecnologie Informatiche     
Bertolazzi E., Manzini G. Polynomial Reconstructions and Limiting Strategies in Finite Volume Approximations. Preprint ercim.cnr.ian//2002-1289, 2002.
In this conference paper we focus on the polynomial reconstruction process in multidimensional unstructured Finite Volume methods and the related numerical oscillation Gibbs phenomenon. For the sake of exposition, we address the formally second-order accurate linear reconstruction in a cell-centered Finite Volume method, applied to the resolution of the time-dependent scalar advection equation. Because of the simplicity of this model problem, we can quantify the anti-diffusive effect of the reconstruction process and outline how numerical oscillations are related to a discrete version of an $L^2$ stability condition satisfied by the continuous solution. This condition is less restrictive than the local maximum principle which is usually required in discrete schemes to prevent the formation of spurious oscillations. Finally, we illustrate both theoretically and experimentally that a simple constraint in the limiter design makes possible a quite effective strategy in controlling numerical oscillations, which is promising for more complex applications.
Subject Finite Volumes, non-oscillatory reconstructions, limiters.

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