Robust a posteriori error estimates for reaction–diffusion problems


Errors (left) and estimators (right), boundary layer


Error, error components, and estimators (left) and effectivity index (right), counter-example for no weights/submesh

Main results:

  • steady linear reaction–diffusion equation;
  • arbitrary-order finite element approximation, arbitrary space dimension;
  • a posteriori error estimates:
    • guaranteed upper bound in the energy norm;
    • local efficiency;
    • robustness with respect to reaction dominance;
  • inexpensive construction (weights; no submesh, no combination with residual estimates);
  • counter-example where estimates with no weights/submesh/combination fail;
  • explicit bounds for inverse inequality constants on a simplex.

Details: paper (preprint) with Iain Smears, presentation.

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