Analysis of a variable time-step discretization for a phase transition model with micro-movements

Ulisse Stefanelli

doi:10.3934/cpaa.2006.5.659

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2006, Volume 5, Issue 3: 659-673. Doi: 10.3934/cpaa.2006.5.659

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Analysis of a variable time-step discretization for a phase transition model with micro-movements

Ulisse Stefanelli^1,

1.
Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, via Ferrata 1, 27100 Pavia

Received: March 2005

Revised: January 2006

Published: September 2006

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Abstract

This note deals with a semi-implicit time discretization with variable time-step of a phase transition model taking into account the microscopic movements of molecules. In particular, we focus on the study of an unconditionally stable and convergent approximation. Moreover, an a priori estimate for the discretization error is established.

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Mathematics Subject Classification: Primary: 80A22; Secondary: 35K55, 65M15.

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Analysis of a variable time-step discretization for a phase transition model with micro-movements

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