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Analytical validation of the Finite Element Method model for Laplace equation

Węgrzyn-Skrzypczak Ewa, Skrzypczak Tomasz

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 3

97--106

The presented paper is focused on the comparison of the numerical solution of the Laplace equation in a two-dimensional space with the results obtained with the use of the analytical method. The results of the numerical model are computed on the base of the Finite Element Method. The analytical solution of the considered equation is obtained using the Fourier series. Finally the results of both methods are compared in order to verify the accuracy of numerical implementation.

Analytical and numerical solution of the heat conduction problem in the rod

Węgrzyn-Skrzypczak E., Skrzypczak T.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 4

79--86

In this paper, the results of analytical and numerical solution of the problem of heat transport in the rod of finite length are presented. The analytical solution is obtained with the use of the Fourier series. The numerical model of the problem is based on the Finite Element Method (FEM). In addition, to check the compatibility of both solutions, distributions of the temperature for selected time moments are compared and discussed.

Zastosowanie równań różniczkowych cząstkowych drugiego stopnia w zagadnieniach technicznych

Biały J., Gołębiowski J.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Sił Powietrznych

2013

Nr 1

9--21

Niniejszy artykuł ma za zadanie przybliżyć zagadnienie dotyczące rozwiązania równania struny i membrany metodą Fouriera, pokazać sposób jej wykorzystania w różnych dziedzinach.

The following article is intended to focus on the problem pertaining to the solution of string and membrane equation with Fourier’s method as well as to show its applications in various fields.

The Influence of Physical Parameters in Discrete-continuous Systems with Articulated Joins on Solution of Boundary and Initial Problems by Fourier’s Method

Łopata A., Ozga A.

Vibrations in Physical Systems

2004

Vol. 21

247--250