Robust a posteriori error estimates for linear advection problems


Errors (left) and estimators (right), discontinuous solution with aligned triangulation

Main results:

  • steady linear advection equation;
  • rigorous results in 1D, heuristic extensions to mD;
  • a posteriori error estimates:
    • guaranteed upper bound in the L2 norm;
    • local efficiency;
    • robustness with respect to advection dominance and polynomial degree;
  • numerically asymptotic exactness.

Details: paper (preprint) with Alexandre Ern and Mohammad Zakerzadeh.

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