On the Stability of Evolution Galerkin Schemes Applied to a Two-Dimensional Wave Equation System

The subject of the paper is the analysis of stability of the evolution Galerkin (EG) methods for the two-dimensional wave equation system. We apply von Neumann analysis and use the Fourier transformation to estimate the stability limits of both the first and the second order EG methods.

[1]  S. Ostkamp,et al.  Multidimensional characteristic Galerkin methods for hyperbolic systems , 1997 .

[2]  Michael Fey,et al.  Multidimensional Upwinding. Part I. The Method of Transport for Solving the Euler Equations , 1998 .

[3]  Mária Lukácová-Medvid'ová,et al.  Well-balanced finite volume evolution Galerkin methods for the shallow water equations , 2015, J. Comput. Phys..

[4]  Gerald Warnecke,et al.  Finite volume evolution Galerkin methods for nonlinear hyperbolic systems , 2002 .

[5]  Richard Courant,et al.  Supersonic Flow And Shock Waves , 1948 .

[6]  R. LeVeque.  Wave Propagation Algorithms for Multidimensional Hyperbolic Systems , 1997 .

[7]  G. Warnecke,et al.  On the boundary conditions for EG methods applied to the two‐dimensional wave equation system , 2004 .

[8]  Mária Lukácová-Medvid'ová,et al.  Evolution Galerkin methods for hyperbolic systems in two space dimensions , 2000, Math. Comput..

[9]  Philip L. Roe,et al.  Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics , 1986 .

[10]  Tim Kröger,et al.  An evolution Galerkin scheme for the shallow water magnetohydrodynamic equations in two space dimensions , 2005 .

[11]  Gerald Warnecke,et al.  Finite Volume Evolution Galerkin Methods for Multidimensional Hyperbolic Systems , 2001 .

[12]  Endre Süli,et al.  Euler characteristic Galerkin scheme with recovery , 1993 .

[13]  Gerald Warnecke,et al.  Finite volume evolution Galerkin methods for Euler equations of gas dynamics , 2002 .

[14]  Endre Süli,et al.  Characteristic Galerkin Schemes for Scalar Conservation Laws in Two and Three Space Dimensions , 1997 .

[15]  Gerald Warnecke,et al.  On Evolution Galerkin Methods for the Maxwell and the Linearized Euler Equations , 2004 .

[16]  Gerald Warnecke,et al.  Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system , 2003 .

[17]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[18]  G. Warnecke.  Finite Volume Evolution Galerkin ( FVEG ) Methods for Hyperbolic Systems , .

[19]  Mária Lukácová-Medvid'ová,et al.  Finite Volume Evolution Galerkin Methods for Hyperbolic Systems , 2004, SIAM J. Sci. Comput..

[20]  Gerald Warnecke,et al.  Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system , 2007 .

[21]  S. Noelle.  The MoT-ICE: a new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on Fey's method of transport , 2000 .

[22]  Sophie Depeyre,et al.  A stability analysis for finite volume schemes applied to the Maxwell system , 1999 .

[23]  Michael Fey,et al.  Multidimensional Upwinding. Part II. Decomposition of the Euler Equations into Advection Equations , 1998 .