Stability of the P_2 semi-Lagrangian scheme

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 P_2 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.

arXiv comment16 pages, 3 figures