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A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method for wave propagation

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Published 3 August 2011 • 2011 The Japan Society of Fluid Mechanics and IOP Publishing Ltd
, , Citation Keisuke Sawada and Kanako Yasue 2011 Fluid Dyn. Res. 43 041402 DOI 10.1088/0169-5983/43/4/041402

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1 Department of Aerospace Engineering, Tohoku University, Sendai 980-8579, Japan

Dates

  1. Received 8 January 2010
  2. Published

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Abstract

A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method proposed in our previous work was carried out for a scalar advection equation using three different generating patterns of triangular cells in two-dimensional space. A detailed mathematical formulation of the stability analysis is presented in this paper. It is shown that the present cell-wise implicit method with spatial accuracies up to fourth order is stable with very large Courant–Friedrichs–Lewy (CFL) numbers.

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10.1088/0169-5983/43/4/041402