scholarly journals Exact Artificial Boundary Conditions for Quasi-Linear Problems in Semi-Infinite Strips

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yajun Chen ◽  
Qikui Du
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Artificial Boundary ◽  
Numerical Examples ◽  
Artificial Boundary Conditions ◽  
Kirchhoff Transformation ◽  
Approximate Boundary Conditions ◽  
Linear Problems

In this paper, the exact artificial boundary conditions for quasi-linear problems in semi-infinite strips are investigated. Based on the Kirchhoff transformation, the exact and approximate boundary conditions on a segment artificial boundary are derived. The error estimate for the finite element approximation with the artificial boundary condition is obtained. Some numerical examples show the efficiency of this method.

scholarly journals Solution of Exterior Quasilinear Problems Using Elliptical Arc Artificial Boundary

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1598
Author(s):  
Yajun Chen ◽  
Qikui Du
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Numerical Experiments ◽  
Bounded Region ◽  
The Finite Element Method ◽  
Artificial Boundary ◽  
Artificial Boundary Condition ◽  
Artificial Boundary Conditions ◽  
Kirchhoff Transformation ◽  
Quasilinear Problems

In this paper, the method of artificial boundary conditions for exterior quasilinear problems in concave angle domains is investigated. Based on the Kirchhoff transformation, the exact quasiliner elliptical arc artificial boundary condition is derived. Using the approximate elliptical arc artificial boundary condition, the finite element method is formulated in a bounded region. The error estimates are obtained. The effectiveness of our method is showed by some numerical experiments.

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