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\(P_0\) time/space subcell limiting DG-DGLM method for hyperbolic systems of conservation laws. (English) Zbl 1524.65595

Summary: A high order discontinuous Galerkin method with Lagrange multiplier (DGLM) in space combined with discontinuous Galerkin (DG) method in time (DG-DGLM) [M.-Y. Kim, Comput. Math. Appl. 75, No. 12, 4458–4489 (2018; Zbl 1419.65065)] is numerically investigated for the approximation of the solution to the system of hyperbolic conservation laws. Computation is done in element by element fashion. \(P_0\) time and space subcell limiting processes are applied to resolve the shocks. It is numerically shown that the high order DG-DGLM method is well-suited for long time integrations. Several numerical experiments for advection, shallow water, and compressible Euler equations are presented to show the performance of the high order DG-DGLM with \(P_0\) time and space subcell limiting processes.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q31 Euler equations

Citations:

Zbl 1419.65065

Software:

HE-E1GODF; SWASHES
PDFBibTeX XMLCite
Full Text: DOI

References:

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