Object-Oriented Implementation of Finite Element Methodology

Author(s):  
Ashok V. Kumar ◽  
Lichao Yu

Abstract A modular object-oriented framework for finite element method is presented. The framework represents an abstract implementation of the finite element methodology. This ensures that minimal changes are required when extending the software to add new element type and analysis capability. The modular nature of the framework enables easy maintanence and reuse of the software. Furthermore, it ensures that the changes required for extension and maintanence of the software are local in nature. The framework was implemented to show the effectiveness of the approach and tested by implementing simple elements and solvers. The potential for easy extension of the software to cover all varieties of boundary value problems and solver algorithms is discussed.

2012 ◽  
Vol 182-183 ◽  
pp. 1571-1574
Author(s):  
Qi Sheng Wang ◽  
Jia Dao Lai

In this paper, the weighed error estimation of finite element method for the two-point boundary value problems are discussed. Respectively, the norm estimation of the H1 and L2 are obtained.


2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran

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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