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phase relaxation

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Error Control and Andaptivity for a Phase Relaxation Model
Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 4 / July 2000

Published online by Cambridge University Press:

15 April 2002, pp. 775-797

Print publication:

July 2000
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The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperatureθ and an ODE with double obstaclesfor phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requiresthe stability constraint τ ≤ ε. Conforming piecewiselinear finite elements over highly graded simplicial mesheswith parameter h are further employed for space discretization.A posteriori errorestimates are derived for both unknowns θ and χ, whichexhibit the correct asymptotic order in terms of ε, h andτ. This result circumvents the use of duality, which does noteven apply in this context.Several numerical experiments illustrate the reliability of theestimators and document the excellent performance of the ensuingadaptive method.

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Error Control and Andaptivity for a Phase Relaxation Model

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Error Control and Andaptivity for a Phase Relaxation Model