High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws

Mi Young Kim, Eun-Jae Park, Jaemin Shin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this work, we present novel high-order discontinuous Galerkin methods with Lagrange multiplier (DGLM) for hyperbolic systems of conservation laws. Lagrange multipliers are introduced on the inter-element boundaries via the concept of weak divergence. Static condensation on element unknowns considerably reduces globally coupled degrees of freedom, resulting in the stiffness equations in the Lagrange multipliers only. We first establish stability results and provide conditions on the stabilization parameter, which plays an important role in resolving discontinuities as well. Accuracy tests are then performed, which shows optimal convergence in the L2 norm. Extensive numerical results indicate that the DGLM has potentials in delivering high order accurate information for various problems in hyperbolic conservation laws. Numerical examples include inviscid Burgers’ equations, shallow water equations (subcritical flow and supercritical upstream, subcritical downstream flow, and 2D circular dam break), and compressible Euler equations (Intersection of Mach 3 and Sod's shock tube).

Original languageEnglish
Pages (from-to)1945-1974
Number of pages30
JournalComputers and Mathematics with Applications
Volume73
Issue number9
DOIs
Publication statusPublished - 2017 May 1

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Hyperbolic Systems of Conservation Laws
Lagrange multipliers
Discontinuous Galerkin Method
Galerkin methods
Conservation
Higher Order
Dam Break
Superoxide Dismutase
Shock Tube
Compressible Euler Equations
Hyperbolic Conservation Laws
Shock tubes
Euler equations
Shallow Water Equations
Degrees of freedom (mechanics)
Burgers Equation
Condensation
Dams
Mach number
Boundary Elements

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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High-order discontinuous Galerkin methods with Lagrange multiplier for hyperbolic systems of conservation laws. / Kim, Mi Young; Park, Eun-Jae; Shin, Jaemin.

In: Computers and Mathematics with Applications, Vol. 73, No. 9, 01.05.2017, p. 1945-1974.

Research output: Contribution to journalArticle

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