Multigrid algorithms for hp-Discontinuous Galerkin discretizations of elliptic problems

2013/10/24 by Paola F. Antonietti, Antonietti, P. F., Marco Sarti +3 · 4 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1310.6573

openalex publication_date 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present W-cycle multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp-version discontinuous Galerkin discretizations of elliptic problems. Starting from a classical framework in multigrid analysis, we define a smoothing and an approximation property, which are used to prove the uniform convergence of the W-cycle scheme with respect to the granularity of the grid and the number of levels. The dependence of the convergence rate on the polynomial approximation degree p is also tracked, showing that the contraction factor of the scheme deteriorates with increasing p. A discussion on the effects of employing inherited or non-inherited sublevel solvers is also presented. Numerical experiments confirm the theoretical results.

Citations

• An Interior Penalty Finite Element Method with Discontinuous Elements
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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• p-multigrid method for the discontinuous Galerkin discretization of elliptic problems
• A Geometric Multigrid Preconditioner for Discontinuous Galerkin Shifted Boundary Method

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