The box method for elliptic interface problems on locally refined meshes

1994 ◽  
pp. 177-186 ◽  
Author(s):  
Bernd Heinrich
Keyword(s):  
Interface Problems ◽  
Elliptic Interface Problems ◽  
Refined Meshes ◽  
Box Method ◽  
Locally Refined Meshes

scholarly journals A stabilized coupled method and its optimal error estimates for elliptic interface problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jiaping Yu ◽  
Feng Shi ◽  
Jianping Zhao
Keyword(s):  
Error Estimates ◽  
Numerical Experiments ◽  
Interface Problems ◽  
Optimal Error Estimates ◽  
Computational Stability ◽  
Optimal Error ◽  
Stabilized Method ◽  
Elliptic Interface Problems ◽  
Coupled Method

Abstract In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provided to show the optimal error estimates of this stabilized method. Several numerical experiments are carried out to demonstrate the computational stability and effectiveness of the method.

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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