Gradient schemes for linear and non-linear elasticity equations

Jerome Droniou, Bishnu P Lamichhane

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

The gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the gradient scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full H2-regularity or for non-linear models.
Original languageEnglish
Pages (from-to)251-277
Number of pages27
JournalNumerische Mathematik
Volume129
Issue number2
DOIs
Publication statusPublished - 2015

Keywords

  • 65N12
  • 65N15
  • 65N30

Cite this

Droniou, Jerome ; Lamichhane, Bishnu P. / Gradient schemes for linear and non-linear elasticity equations. In: Numerische Mathematik. 2015 ; Vol. 129, No. 2. pp. 251-277.
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Gradient schemes for linear and non-linear elasticity equations. / Droniou, Jerome; Lamichhane, Bishnu P.

In: Numerische Mathematik, Vol. 129, No. 2, 2015, p. 251-277.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - Gradient schemes for linear and non-linear elasticity equations

AU - Droniou, Jerome

AU - Lamichhane, Bishnu P

PY - 2015

Y1 - 2015

N2 - The gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the gradient scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full H2-regularity or for non-linear models.

AB - The gradient scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the gradient scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the gradient scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full H2-regularity or for non-linear models.

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KW - 65N15

KW - 65N30

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DO - 10.1007/s00211-014-0636-y

M3 - Article

VL - 129

SP - 251

EP - 277

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

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