Skip to main content

Research Repository

Advanced Search

An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix

Barrett, J.W.; Blowey, J.F.

Authors

J.W. Barrett



Abstract

Using a slightly different discretization scheme in time and adapting the approach in Nochetto et al. (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowley (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piecewise linear finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix and (i) a logarithmic free energy, and (ii) a non-smooth free energy (the deep quench limit); respectively. Moreover, the improved error bound in the deep quench limit is optimal. Numerical experiments with three components illustrating the above error bounds are also presented.

Citation

Barrett, J., & Blowey, J. (2001). An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix. Numerische Mathematik, 88(2), 255-297. https://doi.org/10.1007/pl00005445

Journal Article Type Article
Online Publication Date Apr 1, 2001
Publication Date Apr 1, 2001
Deposit Date Apr 23, 2007
Journal Numerische Mathematik
Print ISSN 0029-599X
Electronic ISSN 0945-3245
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 88
Issue 2
Pages 255-297
DOI https://doi.org/10.1007/pl00005445

You might also like



Downloadable Citations