Geodesic
Adaptive Crouzeix–Raviart boundary element method
Heuer, Norbert1 ; Karkulik, Michael1
1 Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna, 4860 Santiago, Chile.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1193-1217

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For the nonconforming Crouzeix–Raviart boundary elements from [N. Heuer and F.-J. Sayas, Numer. Math. 112 (2009) 381–401], we develop and analyze a posteriori error estimators based on the h-h/2 methodology. We discuss the optimal rate of convergence for uniform mesh refinement, and present a numerical experiment with singular data where our adaptive algorithm recovers the optimal rate while uniform mesh refinement is sub-optimal. We also discuss the case of reduced regularity by standard geometric singularities to conjecture that, in this situation, non-uniformly refined meshes are not superior to quasi-uniform meshes for Crouzeix–Raviart boundary elements.

Reçu le :
DOI : 10.1051/m2an/2015003
Classification : 65N30, 65N38, 65N50, 65R20
Keywords: Boundary element method, adaptive algorithm, nonconforming method, a posteriori error estimation

Heuer, Norbert 1 ; Karkulik, Michael 1

1 Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna, 4860 Santiago, Chile. 
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     title = {Adaptive {Crouzeix{\textendash}Raviart} boundary element method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1193--1217},
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Heuer, Norbert; Karkulik, Michael. Adaptive Crouzeix–Raviart boundary element method. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 1193-1217. doi: 10.1051/m2an/2015003

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