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• W1994593866 abstract "Solutions of the so-called prescribed curvature problem $min _{Asubseteq Omega } mathcal {P}_ Omega (A) - int _A g(x)$, $g$ being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers $A subset subset Omega$ we prove an $mathcal {O}( epsilon ^2 |log epsilon |^2)$ error estimate (where $epsilon$ stands for the perturbation parameter), and show that this estimate is quasi-optimal. The proof is based on the construction of accurate barriers suggested by formal asymptotics. This analysis is next extended to a finite element discretization of the PDE to prove the same error estimate for discrete minima." @default.
• W1994593866 created "2016-06-24" @default.
• W1994593866 creator A5073262759 @default.
• W1994593866 date "1997-01-01" @default.
• W1994593866 modified "2023-09-26" @default.
• W1994593866 title "A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem" @default.
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• W1994593866 doi "https://doi.org/10.1090/s0025-5718-97-00771-0" @default.
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