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Backward difference time discretization of parabolic differential equations on evolving surfaces

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posted on 2023-06-08, 15:20 authored by Christian Lubich, Dhia Mansour, Chandrasekhar VenkataramanChandrasekhar Venkataraman
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 (BDF). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semi-discretization, stability of the full discretization is proven for the BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

4

Volume

33

Page range

1365-1385

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-07-08

First Open Access (FOA) Date

2013-07-08

First Compliant Deposit (FCD) Date

2013-07-08

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