Residual-based a posteriori error estimation for stochastic magnetostatic problems

D.H. Mac ^[1] ; Z. Tang ^[2] ; S. Clénet ^[1] ; E. Creusé ^[3]
1. [1] Inria research centre Lille - Nord Europe
  
  Inria research centre Lille - Nord Europe
  
  Arrondissement de Lille, Francia
2. [2] University of Lille Nord de France
  
  University of Lille Nord de France
  
  Arrondissement de Lille, Francia
3. [3] Université Lille Nord de France & INRIA Lille Nord Europe, France
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 51-67
Idioma: inglés
DOI: 10.1016/j.cam.2015.03.027
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Resumen
- In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.