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.

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