Eta%-Superconvergence in the Interior of Locally Refined Meshes of Quadrilaterals: Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations

1994 ◽  
Author(s):  
I. Babuska ◽  
T. Strouboulis ◽  
S. K. Gangaraj ◽  
C. S. Upadhyay
Keyword(s):  
Finite Element ◽  
Refined Meshes ◽  
Locally Refined Meshes

scholarly journals Discrete extension operators for mixed finite element spaces on locally refined meshes

2016 ◽  
Vol 85 (302) ◽  
pp. 2639-2650 ◽  
Author(s):  
Mark Ainsworth ◽  
Johnny Guzmán ◽  
Francisco-Javier Sayas
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Refined Meshes ◽  
Locally Refined Meshes

ADI-CRSTS: A New Method for the Moving Heat Sources — Application to a Train Pantograph Strip

2017 ◽  
Author(s):  
Nicolas Delcey ◽  
Philippe Baucour ◽  
Didier Chamagne ◽  
Geneviève Wimmer ◽  
Odile Bouger ◽  
...  
Keyword(s):  
Thermal Flux ◽  
Computation Time ◽  
Point Of View ◽  
Heat Sources ◽  
Physical Point ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Refined Meshes ◽  
Physical Phenomena ◽  
Locally Refined Meshes

The pantograph strip interface involves many physical phenomena. Temperature evolution is one of them. This problem includes various thermal flux and sources. More specifically, due to the train motion, a moving zigzag heat source occurs. This paper deals with a thermal 2D Alternating Direction Implicit (ADI) numerical method for temperature estimations in the train pantograph carbon strip, the aims being a better wear problems anticipation and the creation of a preventive maintenance. For that, an electrical model is coupled to the thermal one to take into account all Joule effects. The ADI strategy enables a significant computation time reduction against most classical resolution methods. Besides, the model involves two mathematical processes: the first one is an appropriate variable transform which induces a fixed surface heat production, while the second is based on locally refined meshes. Various numerical tests are presented and discussed in order to show the accuracy of the scheme. From a physical point of view, the results are much interesting. Further investigations, depending on the different parameters, should lead us to predict the strip critical thermal phases.

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