A priori and a posteriori W1,∞error analysis of a QC method for complex lattices

Assyr Abdulle; Ping Lin; Alexander V. Shapeev

doi:10.1137/120894300

A priori and a posteriori W^1,∞error analysis of a QC method for complex lattices

Assyr Abdulle
, Ping Lin
, Alexander V. Shapeev

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

5 Citations (Scopus)

Abstract

In this paper we derive regularity results for equilibria of multilattices under an
external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We
illustrate our error estimates with numerical experiments.

Original language	English
Pages (from-to)	2357-2379
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	51
Issue number	4
DOIs	https://doi.org/10.1137/120894300
Publication status	Published - 2013

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10.1137/120894300

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title = "A priori and a posteriori W1,∞error analysis of a QC method for complex lattices",

abstract = "In this paper we derive regularity results for equilibria of multilattices under an external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We illustrate our error estimates with numerical experiments.",

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AU - Abdulle, Assyr

AU - Lin, Ping

AU - Shapeev, Alexander V.

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N2 - In this paper we derive regularity results for equilibria of multilattices under an external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We illustrate our error estimates with numerical experiments.

AB - In this paper we derive regularity results for equilibria of multilattices under an external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We illustrate our error estimates with numerical experiments.

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DO - 10.1137/120894300

M3 - Article

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EP - 2379

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

A priori and a posteriori W1,∞error analysis of a QC method for complex lattices

Abstract

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A priori and a posteriori W^1,∞error analysis of a QC method for complex lattices