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.
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 (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: