Formulation of Finite Element Method for 1-D
Poisson Equation

Mrs. Pallavi P. Chopade; Dr. Prabha S. Rastogi

doi:https://doi.org/10.14445/22315373/IJMTT-V56P548

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 5 | Year 2018 | Article Id. IJMTT-V56P548 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P548

Formulation of Finite Element Method for 1-D Poisson Equation

Mrs. Pallavi P. Chopade, Dr. Prabha S. Rastogi

Abstract

This paper focuses on the use of solving electrostatic one-dimension Poisson differential equation boundary-value problem. Sample problems that introduce the finite element methods are presented here and evaluated with analytical and numerical approaches. These approaches are developed in MATLAB and their solutions are compared and verified. Error analysis is also presented in this paper where the numerical error is compute dusing two different definitions namely the percent error and the error based on the L2 norm. this numerical error is reduced by increasing in number of elements.

Keywords

Boundary-value problems, Differential equation, Electrostatics, Finite Element Method, Poisson’s equation.

References

[1]. Lonngren, K.E., Savov, S.V. and Jost, R.J., 2007.Fundamentals of Electromagnetics with MATLAB. Scitech publishing.
[2]. Papanikos, G. and Gousidou-Koutita, M.C., 2015. A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic PartialDifferential Equations.Applied Mathematics,6(12), p.2104.
[3]. Chaudhari, T.U. and Patel, D.M., 2015. Finite Element Solution of Poisson’s equation in a homogeneous medium.
[4]. Brenner, S. and Scott, R., 2007.The mathematical theory of finite element methods(Vol. 15). Springer Science & Business Media.
[5]. Sharma, N., Formulation of Finite Element Method for 1D and 2D Poisson Equation.
[6]. Agbezuge, L., 2006. Finite Element Solution of the Poisson equation with Dirichlet Boundary Conditions in a rectangular domain.
[7]. Jain, M.K., 2003.Numerical methods for scientific and engineering computation. New Age International.
[8]. Rao, N., 2008.Fundamentals of Electromagnetics for Engineering. Pearson Education India.
[9]. Sadiku, M.N., 2011.Numerical techniques in electromagnetics with MATLAB. CRC press.
[10]. Yang, W.Y., Cao, W., Chung, T.S. and Morris, J., 2005.Applied numerical methods using MATLAB. John Wiley & Sons.

Citation :

Mrs. Pallavi P. Chopade, Dr. Prabha S. Rastogi, "Formulation of Finite Element Method for 1-D Poisson Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 5, pp. 360-365, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P548