A Galerkin Finite Elements Method for A Model Problem
Abstract
This study is going to deal with the application of the Galerkin finite elements method in order to find the approximate numerical solutions of a model problem based on Hermite B-Spline basis functions, which have been widely used in recent years. Along with this study, it is aimed to contribute a new study to the literature based on Hermite B-spline basis functions, which differ from the classical B-spline basis functions commonly used in the literature, by using the Galerkin finite elements method. With the current study, it is also aimed to apply the presented method and Hermite B-spline basis fucntions to a wide range of ordinary differential equations and/or partial differential equations even fractional order differential equations. Therefore, it is considered to be a preliminary study for fast reaction or slow reaction problems encountered in many different fields of engineering.
Keywords
Hermite Galerkin Method (HGM), Finite Element Method (FEM), Differential Equation, Error Norms
References
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