Symbolic-Numerical Solution of Boundary-Value Problems with Self-adjoint Second-Order Differential Equation Using the Finite Element Method with Interpolation Hermite Polynomials

2014 ◽  
pp. 138-154 ◽  
Author(s):  
Alexander A. Gusev ◽  
Ochbadrakh Chuluunbaatar ◽  
Sergue I. Vinitsky ◽  
Vladimir L. Derbov ◽  
Andrzej Góźdź ◽  
...  
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Hermite Polynomials ◽  
The Finite Element Method ◽  
Second Order Differential Equation

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

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