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.