Spacetime meshing with adaptive refinement and coarsening

Reza Abedi, Shuo Heng Chung, Jeff G Erickson, Yong Fan, Michael Garland, Damrong Guoy, Robert Haber, John M. Sullivan, Shripad Thite, Yuan Zhou

Research output: Contribution to conferencePaperpeer-review


We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain Ω and a target time value T, our method constructs a tetrahedral mesh of the spacetime domain Ω × [0, T] in constant running time per tetrahedron in ℝ 3 using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries.

Original languageEnglish (US)
Number of pages10
StatePublished - Sep 29 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: Jun 9 2004Jun 11 2004


OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/TerritoryUnited States
CityBrooklyn, NY


  • Adaptivity
  • Advancing front
  • Mesh generation
  • Spacetime discontinuous Galerkin
  • Tetrahedral meshes
  • Unstructured meshes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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