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Titre
High-Order AFEM for the Laplace–Beltrami Operator: Convergence Rates
Autor(es)
Sujet
Numerical analysis
Laplace–Beltrami operator
Parametric surfaces
Adaptive Finite Element methods
Convergence rates
A posteriori error estimates
Higher order
Fecha de publicación
2016-11-23
Éditeur
Springer Nature
Citación
A. Bonito, J.M. Cascón, K. Mekchay, P. Morin, R.H. Nochetto. (2016) High-Order AFEM for the Laplace-Beltrami Operator: Convergence Rates. Foundations of Computational Mathematics. Vol 16 (6), pp 1473-1539
Serie / N.º
Foundations of Computational Mathematics;Volume 16, Issue 6
Résumé
We present a new AFEM for the Laplace–Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W1∞ and piecewise in a suitable Besov class embedded in C1,α with α∈(0,1]. The idea is to have the surface sufficiently well resolved in W∞1 relative to the current resolution of the PDE in H1. 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 and PDE error in H1.
URI
ISSN
1615-3375
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