An asymptotic analysis is developed, which guarantees that the equation εa(x)∂uε/∂t = ε divx(a(x)▽xuε) - ψ(uε)/2εa(x) in Rn × (0, T), approximates a flow by mean curvature with an error of order O(ε2). The dependence on space of the relaxation parameter εa(x) is crucial for the stability and accuracy of the finite element approximations based on a local mesh refinement strategy. Several numerical experiments simulate the mean curvature motion of various surfaces and confirm the reliability of the asymptotic analysis.

Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter / M. Paolini, C. Verdi. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 5:6(1992), pp. 553-574.

Asymptotic and numerical analyses of the mean curvature flow with a space-dependent relaxation parameter

C. Verdi
Ultimo
1992

Abstract

An asymptotic analysis is developed, which guarantees that the equation εa(x)∂uε/∂t = ε divx(a(x)▽xuε) - ψ(uε)/2εa(x) in Rn × (0, T), approximates a flow by mean curvature with an error of order O(ε2). The dependence on space of the relaxation parameter εa(x) is crucial for the stability and accuracy of the finite element approximations based on a local mesh refinement strategy. Several numerical experiments simulate the mean curvature motion of various surfaces and confirm the reliability of the asymptotic analysis.
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/187376
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