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• W2964290469 startingPage "1473" @default.
• W2964290469 abstract "We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally $$W^1_infty $$ and piecewise in a suitable Besov class embedded in $$C^{1,alpha }$$ with $$alpha in (0,1]$$ . The idea is to have the surface sufficiently well resolved in $$W^1_infty $$ relative to the current resolution of the PDE in $$H^1$$ . This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in $$W^1_infty $$ and PDE error in $$H^1$$ ." @default.
• W2964290469 created "2019-07-30" @default.
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• W2964290469 date "2016-11-23" @default.
• W2964290469 modified "2023-10-18" @default.
• W2964290469 title "High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates" @default.
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• W2964290469 doi "https://doi.org/10.1007/s10208-016-9335-7" @default.
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