p-robust multilevel algebraic error estimator & solver


Comparative performance (number of iterations and elapsed time) of the a-posteriori-steered p-robust multilevel solvers

Main results:

  • multilevel a posteriori estimator of the algebraic error;
  • guaranteed (reliable) and efficient:
  • polynomial-degree robust: β independent of p;
  • gives rise to a multilevel iterative algebraic solver with contraction independent of the polynomial degree p:
  • equivalence estimator – solver: α = √ (1 – β2);
  • adaptive number of smoothing steps / adaptive smoothing possible.


  • global coarsest-level solve of lowest-order (p=1);
  • local patchwise contributions from other levels;
  • corresponds to V-cycle geometric multigrid with zero pre– and one (or adaptive number of) post-smoothing steps by block-Jacobi;
  • optimal step size for the descent direction.

Details in Ph.D. thesis of Ani Miraçi, Ph.D. defense presentation; with Jan Papež:

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