High-Order AFEM for the Laplace-Beltrami Operator: Convergence Rates Academic Article

abstract

• 2016, SFoCM. We present a new AFEM for the LaplaceBeltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W1 and piecewise in a suitable Besov class embedded in C1, with (0 , 1 ]. The idea is to have the surface sufficiently well resolved in W1 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 W1 and PDE error in H1.

authors

• Bonito, Andrea

published proceedings

• FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

author list (cited authors)

• Bonito, A., Manuel Cascon, J., Mekchay, K., Morin, P., & Nochetto, R. H.

citation count

• 11

complete list of authors

• Bonito, Andrea||Manuel Cascon, J||Mekchay, Khamron||Morin, Pedro||Nochetto, Ricardo H

publication date

• December 2016

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

keywords

• A Posteriori Error Estimates
• Adaptive Finite Element Method
• Convergence Rates
• Higher Order
• Laplace-beltrami Operator
• Parametric Surfaces

Digital Object Identifier (DOI)

• 10.1007/s10208-016-9335-7

start page

• 1473

end page

• 1539

volume

• 16

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs10208-016-9335-7