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Error Estimates for a Variable Time-Step Discretization of a Phase Transition Model with Hyperbolic Momentum.
- Source :
-
Numerical Functional Analysis & Optimization . Aug/Sep2004, Vol. 25 Issue 5/6, p547-569. 23p. - Publication Year :
- 2004
-
Abstract
- This paper deals with a fully implicit time discretization scheme with variable time-step for a nonlinear system modelling phase transition and mechanical deformations in shape memory alloys. The model is studied in the non-stationary case and accounts for local microscopic interactions between the phases introducing the gradients of the phase parameters. The resulting initial-boundary value problem has already been studied by the author who proved existence, uniqueness and continuous dependence on data for a suitable weak solution along some regularity results. A careful and detailed investigation of the variable time-step discretization is the goal of this paper. Thus, we deduce some estimates for the discretization error. These estimates depend only on data, impose no constraints between consecutive time-steps and show an optimal order of convergence. Finally, we prove another regularity result for the solution under stronger regularity assumptions on data. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01630563
- Volume :
- 25
- Issue :
- 5/6
- Database :
- Academic Search Index
- Journal :
- Numerical Functional Analysis & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 15625826
- Full Text :
- https://doi.org/10.1081/NFA-200042240