The Influence of Higher Order FEM Discretisations on Multigrid Convergence
Abstract: Quadratic and even higher order finite elements are interesting candidates for the numerical solution of partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. The systems of equations that arise from the discretisation of the underlying (elliptic) PDEs are often solved by iterative solvers like preconditioned Krylow-space methods, while multigrid solvers are still rarely used – which might be caused by the high effort that is associated with the realisation of the necessary data structures as well as smoothing and intergrid transfer operators. In this note, we discuss the numerical analysis of quadratic conforming finite elements in a multigrid solver. Using the “correct” grid transfer operators in conjunction with a quadratic finite element approximation allows to formulate an improved approximation property which enhances the (asymptotic) behaviour of multigrid: If m denotes the number of smoothing steps, the convergence rates behave asymptotically like O (1/m2) in contrast to O (1/m) for linear FEM.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
The Influence of Higher Order FEM Discretisations on Multigrid Convergence ; volume:6 ; number:2 ; year:2006 ; pages:221-232
Computational methods in applied mathematics ; 6, Heft 2 (2006), 221-232
- Creator
-
Köster, M.
Turek, S.
- DOI
-
10.2478/cmam-2006-0011
- URN
-
urn:nbn:de:101:1-2410261621179.781897014910
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
15.08.2025, 7:27 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Köster, M.
- Turek, S.
Other Objects (12)
H- and P-multigrid methods for higher-order discontinuous Galerkin discretizations : Forschungsbericht
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton‐multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Interactive physically based simulation - efficient higher-order elements, multigrid approaches and massively parallel data structures
Interactive Physically Based Simulation - Efficient Higher-Order Elements, Multigrid Approaches and Massively Parallel Data Structures
Order Convergence & Unbounded Order Convergence in C(X)
Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations
Robust Monolithic Multigrid FEM Solver for Three Field Formulation of Incompressible Flow Problems
A parallel multigrid method for band structure computation of 3D photonic crystals with higher order finite elements
H- and P-multigrid methods for higher-order discontinuous Galerkin discretizations : Forschungsbericht
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton‐multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Interactive physically based simulation - efficient higher-order elements, multigrid approaches and massively parallel data structures
Interactive Physically Based Simulation - Efficient Higher-Order Elements, Multigrid Approaches and Massively Parallel Data Structures
Order Convergence & Unbounded Order Convergence in C(X)
Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations
Robust Monolithic Multigrid FEM Solver for Three Field Formulation of Incompressible Flow Problems
A parallel multigrid method for band structure computation of 3D photonic crystals with higher order finite elements
H- and P-multigrid methods for higher-order discontinuous Galerkin discretizations : Forschungsbericht
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton‐multigrid FEM for the simulation of thixotropic flow problems
Monolithic Newton-multigrid FEM for the simulation of thixotropic flow problems
Interactive physically based simulation - efficient higher-order elements, multigrid approaches and massively parallel data structures
Interactive Physically Based Simulation - Efficient Higher-Order Elements, Multigrid Approaches and Massively Parallel Data Structures
Order Convergence & Unbounded Order Convergence in C(X)
Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations
Robust Monolithic Multigrid FEM Solver for Three Field Formulation of Incompressible Flow Problems