A spacetime discontinuous Galerkin method for hyperbolic heat conduction

S. T. Miller, R. B. Haber

Research output: Contribution to journalArticlepeer-review


Non-Fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation. For applications involving very short length or time scales, hyperbolic conduction models better represent the physical thermal transport processes. This paper reviews the Maxwell-Cattaneo-Vernotte modification of the Fourier conduction law and describes its implementation within a spacetime discontinuous Galerkin (SDG) finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time. A causal, advancing-front meshing procedure enables a patch-wise solution procedure with linear complexity in the number of spacetime elements. An h-adaptive scheme and a special SDG shock-capturing operator accurately resolve sharp solution features in both space and time. Numerical results for one spatial dimension demonstrate the convergence properties of the SDG method as well as the effectiveness of the shock-capturing method. Simulations in two spatial dimensions demonstrate the proposed method's ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place.

Original languageEnglish (US)
Pages (from-to)194-209
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Issue number2
StatePublished - Dec 1 2008


  • Adaptive analysis
  • Discontinuous Galerkin
  • Finite element
  • Hyperbolic heat conduction
  • Shock capturing

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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