Error analysis for an ALE evolving surface finite element method

Charles M. Elliott; Chandrasekhar Venkataraman

doi:10.1002/num.21930

Error analysis for an ALE evolving surface finite element method

Charles M. Elliott
, Chandrasekhar Venkataraman^*

^*Corresponding author for this work

Applied Mathematics

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

Abstract

We consider an arbitrary Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.

Original language	English
Pages (from-to)	459-499
Number of pages	41
Journal	Numerical Methods for Partial Differential Equations
Volume	31
Issue number	2
Early online date	30 Oct 2014
DOIs	https://doi.org/10.1002/num.21930
Publication status	Published - Mar 2015

Keywords

ALE evolving surface finite elements
error analysis
computational examples

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title = "Error analysis for an ALE evolving surface finite element method",

abstract = "We consider an arbitrary Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results. ",

keywords = "ALE evolving surface finite elements, error analysis, computational examples",

author = "Elliott, \{Charles M.\} and Chandrasekhar Venkataraman",

note = "Contract grant sponsor: UK Engineering and Physical Sciences Research Council (EPSRC); EP/G010404 and EP/J016780/1 (to C.V.).",

year = "2015",

month = mar,

doi = "10.1002/num.21930",

language = "English",

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journal = "Numerical Methods for Partial Differential Equations",

issn = "0749-159X",

publisher = "John Wiley \& Sons, Ltd",

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AU - Elliott, Charles M.

AU - Venkataraman, Chandrasekhar

N1 - Contract grant sponsor: UK Engineering and Physical Sciences Research Council (EPSRC); EP/G010404 and EP/J016780/1 (to C.V.).

PY - 2015/3

Y1 - 2015/3

N2 - We consider an arbitrary Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.

AB - We consider an arbitrary Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.

KW - ALE evolving surface finite elements

KW - error analysis

KW - computational examples

U2 - 10.1002/num.21930

DO - 10.1002/num.21930

M3 - Article

SN - 0749-159X

VL - 31

SP - 459

EP - 499

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

Error analysis for an ALE evolving surface finite element method

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