Backward difference time discretization of parabolic differential equations on evolving surfaces

Christian Lubich; Dhia Mansour; Chandrasekhar Venkataraman

doi:10.1093/imanum/drs044

Backward difference time discretization of parabolic differential equations on evolving surfaces

Christian Lubich^*, Dhia Mansour, Chandrasekhar Venkataraman

^*Corresponding author for this work

Applied Mathematics

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

Abstract

A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

Original language	English
Pages (from-to)	1365-1385
Number of pages	21
Journal	IMA Journal of Numerical Analysis
Volume	33
Issue number	4
DOIs	https://doi.org/10.1093/imanum/drs044
Publication status	Published - Oct 2013

Keywords

parabolic PDE
evolving-surface finite element method
backward difference formula
G-stability
multiplier technique
energy estimates

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10.1093/imanum/drs044

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title = "Backward difference time discretization of parabolic differential equations on evolving surfaces",

abstract = "A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.",

keywords = "parabolic PDE, evolving-surface finite element method, backward difference formula, G-stability, multiplier technique, energy estimates",

author = "Christian Lubich and Dhia Mansour and Chandrasekhar Venkataraman",

year = "2013",

month = oct,

doi = "10.1093/imanum/drs044",

language = "English",

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pages = "1365--1385",

journal = "IMA Journal of Numerical Analysis",

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T1 - Backward difference time discretization of parabolic differential equations on evolving surfaces

AU - Lubich, Christian

AU - Mansour, Dhia

AU - Venkataraman, Chandrasekhar

PY - 2013/10

Y1 - 2013/10

N2 - A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

AB - A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

KW - parabolic PDE

KW - evolving-surface finite element method

KW - backward difference formula

KW - G-stability

KW - multiplier technique

KW - energy estimates

U2 - 10.1093/imanum/drs044

DO - 10.1093/imanum/drs044

M3 - Article

SN - 0272-4979

VL - 33

SP - 1365

EP - 1385

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 4

ER -

Backward difference time discretization of parabolic differential equations on evolving surfaces

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Keywords

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