scholarly journals An efficient numerical method for one-dimensional hyperbolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01002
Author(s):  
Chartese Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Method Of Lines ◽  
Interface Problems ◽  
Uniform Mesh ◽  
One Dimensional ◽  
Immersed Finite Element ◽  
New Methods ◽  
The Method Of Lines

In this paper, we develop an efficient numerical scheme for solving one-dimensional hyperbolic interface problems. The immersed finite element (IFE) method is used for spatial discretization, which allows the solution mesh to be independent of the interface. Consequently, a fixed uniform mesh can be used throughout the entire simulation. The method of lines is used for temporal discretization. Numerical experiments are provided to show the features of these new methods.

scholarly journals A high order immersed finite element method for parabolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01007
Author(s):  
Derrick Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Order ◽  
Interface Problems ◽  
Numerical Schemes ◽  
Numerical Examples ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Time Marching ◽  
Element Method

We present a high order immersed finite element (IFE) method for solving 1D parabolic interface problems. These methods allow the solution mesh to be independent of the interface. Time marching schemes including Backward-Eulerand Crank-Nicolson methods are implemented to fully discretize the system. Numerical examples are provided to test the performance of our numerical schemes.

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