Anisotropic Goal-Oriented Mesh Adaptivity in Space and Time for Convection-Dominated Problems

  • Bruchhäuser, Marius Paul (Helmut Schmidt University Hamburg)
  • Bause, Markus (Helmut Schmidt University Hamburg)
  • Endtmayer, Bernhard (Leibniz University Hannover)
  • Margenberg, Nils (Otto von Guericke University Magdeburg)
  • Toulopoulos, Ioannis (University of Western Macedonia)
  • Wick, Thomas (Leibniz University Hannover)

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We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. By employing anisotropic interpolation operators, the estimator is decomposed elementwise with respect to single spatial and temporal directions, naturally leading to adaptive anisotropic mesh refinement. To prevent spurious oscillations in convection-dominated regimes, the streamline upwind Petrov-Galerkin (SUPG) method is applied to stabilize the underlying system in the case of high Peclet numbers. Efficiency and robustness of the underlying algorithm are demonstrated for different goal functionals. The resulting directional error indicators quantify the anisotropy of the solution with respect to the target quantity of interest and generate meshes that efficiently resolve sharp layers. Numerical examples based on established benchmarks for convection-dominated problems illustrate the superiority of the proposed approach over isotropic adaptive and global mesh refinement.