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Relaxing the CFL number of the discontinuous Galerkin method. (English) Zbl 1310.65123

A family of high-order methods for the solution of hyperbolic conservation laws which are based on the discontinuous Galerkin (DG) spatial discretization are proposed. The paper is organized as follows: Section 1 is an introduction. In Section 2, the DG finite element method is introduced and it is shown how it is modified through the introduction of the flux multipliers. The accuracy and stability of modified DG (mDG) are investigated in Sections 3 and 4. In Section 5, the authors apply the mDG scheme to several test examples to confirm the convergence rate and observe the general performance of the scheme in comparison with the standard DG scheme.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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