p-robust multilevel algebraic error estimator & solver

local_global

Comparative performance of the wRAS multilevel solvers with 0 pre- and 1 post-smoothing by block-Jacobi

Main results:

  • multilevel a posteriori estimator of the algebraic error;
  • guaranteed (reliable) and efficient;
  • polynomial-degree robust;
  • gives rise to a multilevel iterative algebraic solver with contraction independent of p;
  • equivalence estimator – solver;

Construction:

  • 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 post-smoothing by block-Jacobi;
  • optimal step size for the descent direction.

Details: preprint with Ani Miraçi and Jan Papež, presentation by Ani Miraçi

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