2022/10/19 by Michael Innerberger, Ani Miraçi, Dirk Praetorius +1 · 1 voice · 1 citation
Mathematics · #math.NA
paper · pdf · doi:10.1051/m2an/2023104
arxiv published 2022/10/19 · arxiv updated 2023/07/19
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that the iterative solver contracts the algebraic error robustly with respect to the polynomial degree p ≥ 1 and the (local) mesh size h. We further prove that the built-in algebraic error estimator which comes with the solver is hp-robustly equivalent to the algebraic error. The application of the solver within the framework of adaptive finite element methods with quasi-optimal computational cost is outlined. Numerical experiments confirm the theoretical findings.