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The discontinuous Galerkin method with Lax–Wendroff type time discretizations. (English) Zbl 1093.76038
Summary: We develop a Lax–Wendroff time discretization procedure for the discontinuous Galerkin method (LWDG) to solve hyperbolic conservation laws. This is a method for time discretization alternative to the popular total variation diminishing Runge-Kutta time discretizations. The LWDG is a one-step, explicit, high-order finite element method. The limiter is performed once at every time step. As a result, LWDG is more compact than Runge-Kutta discontinuous Galerkin method, and the Lax-Wendroff time discretization procedure is more cost effective than Runge-Kutta time discretizations for certain problems including two-dimensional Euler systems of compressible gas dynamics when nonlinear limiters are applied.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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