Solution of Weighted Residual Problems by using Galerkin’s Method

J  Evangeline Cicelia

doi:10.17485/ijst/2014/v7sp3.3

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Solution of Weighted Residual Problems by using Galerkin’s Method

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2014/v7sp3.3

Year: 2020, Volume: 7, Issue: Supplementary 3, Pages: 52–54

Original Article

Solution of Weighted Residual Problems by using Galerkin’s Method

J. Evangeline Cicelia

Department of Mathematics, Bharath Institute of Science & Technology, Bharath University, Selaiyur, Chennai - 600073, Tamil Nadu, India evangelinecicelia@gmail.com

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

For simple one-dimensional problems, direct stiffness method is limited. PMPE (Principle of Minimum Potential Energy) is limited to potential problems and FEM (Finite Element Method) can be applied to many engineering problems that are governed by a differential equation. Hence, there are systematic approaches, needed to generate FE equations, such as Weighted Residual method, Energy method and ordinary differential equation (second-order or fourth-order). Weighted residual method can be solved, in particular using Galerkin’s method.

Keywords: Residual, Weighted, Stiffness, FEM, FE, Galerkin’s Method, Differential Equations