scholarly journals A Partially Penalised Immersed Finite Element Method for Elliptic Interface Problems with Non-Homogeneous Jump Conditions

2018 ◽  
Vol 8 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Haifeng Ji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interface Problems ◽  
Jump Conditions ◽  
Elliptic Interface Problems ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
Element Method

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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