A conservative finite difference scheme for the Falk model system of shape memory alloys

DOI10.1002/zamm.201300177zbMath1336.65144OpenAlexW1955410281MaRDI QIDQ2803448

Shuji Yoshikawa

Publication date: 4 May 2016

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201300177

zbMATH Keywords

finite difference methodshape memory alloysthermoelastic systemdiscrete variational derivative methodFalk's model

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (1)

Structure-preserving finite difference schemes for a semilinear thermoelastic system with second order time derivative

Cites Work

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• Applications of fully conservative schemes in nonlinear thermoelasticity: modelling shape memory materials
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• Hysteresis and phase transitions
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• Analysis of the thermoelastic model of a plate with non-linear shape memory alloy reinforcements
• Asymptotic Behavior of the Solutions to a Landau--Ginzburg System with Viscosity for Martensitic Phase Transitions in Shape Memory Alloys
• Finite element approximations of Landau-Ginzburg's equation model for structural phase transitions in shape memory alloys
• Existance and Uniqueness for Boussinesq type equations on a circle
• Stability of the steady state for the Falk model system of shape memory alloys
• Weak solutions for the Falk model system of shape memory alloys in energy class
• A stable and conservative finite difference scheme for the Cahn-Hilliard equation

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