Optimal anisotropic meshes for minimizing interpolation errors in L p-norm

Long Chen; Pengtao Sun; Jinchao Xu

doi:10.1090/S0025-5718-06-01896-5

Optimal anisotropic meshes for minimizing interpolation errors in L p-norm

Long Chen, Pengtao Sun, Jinchao Xu

Research output: Contribution to journal › Article › peer-review

111 Scopus citations

Abstract

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the Lp norm. Some numerical examples are also given to support the theoretical estimates. © 2006 American Mathematical Society.

Original language	English (US)
Pages (from-to)	179-204
Number of pages	26
Journal	Mathematics of Computation
Volume	76
Issue number	257
DOIs	https://doi.org/10.1090/S0025-5718-06-01896-5
State	Published - Jan 1 2007
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-06-01896-5

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N2 - In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the Lp norm. Some numerical examples are also given to support the theoretical estimates. © 2006 American Mathematical Society.

AB - In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the Lp norm. Some numerical examples are also given to support the theoretical estimates. © 2006 American Mathematical Society.

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JF - Mathematics of Computation

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Optimal anisotropic meshes for minimizing interpolation errors in L p-norm

Abstract

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