Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys

DOI10.1007/BF01385653zbMath0715.65099MaRDI QIDQ751784

Marek Niezgódka, Juergen Sprekels

Publication date: 1991

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133529

zbMATH Keywords

hysteresisfinite elementsshape memory alloysconvergent approximationsnonlinear evolutionary systemsolid-state phase transitionsthermomechanical phase transitions

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Thermodynamics in solid mechanics (74A15) Stefan problems, phase changes, etc. (80A22) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Free boundary problems for PDEs (35R35) Applications to the sciences (65Z05) Chemical kinetics in thermodynamics and heat transfer (80A30)

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Cites Work

• Unnamed Item
• Global solutions to the equations of a Ginzburg-Landau theory for structural phase transitions in shape memory alloys
• Global existence for thermomechanical processes with nonconvex free energies of Ginzburg-Landau form
• Global solutions to a model of structural phase transitions in shape memory alloys
• Global solutions to thermomechanical equations with nonconvex Landau- Ginzberg free energy
• Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
• Stability and optimal control of thermomechanical processes with non‐convex free energies of Ginzburg–Landau type

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