MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs

Innerberger, Michael; Praetorius, Dirk

doi:10.1016/j.amc.2022.127731

Cited by 13 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This section investigates the numerical performance of the proposed multigrid solver of Algorithm 2.1 and the adaptive Algorithm 3.1. The Matlab implementation of the multigrid solver is embedded into the MooAFEM 1 framework from [22]. Throughout, we choose the marking parameter 𝜃 = 0.5 in the adaptive Algorithm 3.1 and 𝑓 = (0, 0) ⊤ .…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In practice, the SOLVE module may become computationally expensive (in contrast to all other modules) when employing a direct solver; see, e.g., [18,22,29] for a discussion of implementational aspects. Thus, usually, an iterative solver is employed to compute an approximation 𝑢 𝐿 of 𝑢 ⋆ 𝐿 on each level, and the exact Galerkin solution 𝑢 ⋆ 𝐿 is not available.…”

Section: Introductionmentioning

confidence: 99%

“…Using the open-source object-oriented 2D Matlab code MooAFEM [22], we present a detailed numerical study of both the algebraic solver and the adaptive algorithm, including higher-order experiments and jumping coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

hp-Robust multigrid solver on locally refined meshes for FEM discretizations of symmetric elliptic PDEs

Innerberger,

Miraçi,

Praetorius

et al. 2024

ESAIM: M2AN

View full text Add to dashboard Cite

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 $p \ge 1$ 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.

show abstract

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%