Stabilized cut discontinuous Galerkin methods for advection reaction problems Articles uri icon

publication date

  • May 2020

start page

  • 2620

end page

  • 2654

issue

  • 5

volume

  • 42

International Standard Serial Number (ISSN)

  • 1064-8275

Electronic International Standard Serial Number (EISSN)

  • 1095-7197

abstract

  • We develop novel stabilized cut discontinuous Galerkin methods for advection-reaction problems. The domain of interest is embedded into a structured, unfitted background mesh in where the domain boundary can cut through the mesh in an arbitrary fashion. To cope with robustness problems caused by small cut elements, we introduce ghost penalties in the vicinity of the embedded boundary to stabilize certain (semi-)norms associated with the advection and reaction operator. A few abstract assumptions on the ghost penalties are identified enabling us to derive geometrically robust and optimal a priori error and condition number estimates for the stationary advection-reaction problem which hold irrespective of the particular cut configuration. Possible realizations of suitable ghost penalties are discussed. The theoretical results are corroborated by a number of computational studies for various approximation orders and for two- and three-dimensional test problems.

subjects

  • Aeronautics
  • Mathematics

keywords

  • advection-reaction problems; discontinuous galerkin; cut finite element method; stabilization; a priori error estimates; condition number