Stability of the P2 semi-Lagrangian scheme
Roberto Ferretti, Michel Mehrenberger
Abstract
Among the various space interpolation operators used in high-order semi-Lagrangian schemes, the case of finite element interpolation presents a somewhat incomplete stability theory, partly due to the impossibility of applying in a standard form the framework of Von Neumann analysis, even in the constant coefficient case. In this work, the stability of the P2 semi-Lagrangian scheme is stated in the case of the constant coefficient equation on a uniform mesh, using a suitable extension of the Von Neumann technique to treat block circulant matrices.
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