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The hp-Multigrid Method Applied to hp-Adaptive Refinement of Triangular Grids

Published

Author(s)

William F. Mitchell

Abstract

Recently the hp version of the finite element method has received increasing attention. This is an adaptive finite element approach in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials. The objective is to determine a distribution of h and p that minimizes the error using the least amount of work in some measure. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method, such as multigrid. An intriguing notion is to use the values of p as the levels of a multilevel method. In this paper we present such a method, known as hp-multigrid, for high order finite elements and hp-adaptive grids. Numerical results suggest the method has a convergence rate of 1/2 for Poisson's equation.
Citation
Numerical Linear Algebra With Applications
Volume
17

Keywords

elliptic partial differential equations, finite elements, hp adaptive refinement, multigrid, p-multigrid

Citation

Mitchell, W. (2010), The hp-Multigrid Method Applied to hp-Adaptive Refinement of Triangular Grids, Numerical Linear Algebra With Applications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=902558 (Accessed June 20, 2024)

Issues

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Created March 16, 2010, Updated June 2, 2021