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The Finite Element Method enables to solve multi-dimensional differential equations on a discrete pattern build from grid points. This finite element mesh together with the finite element method (FEM) approach constitute an effective tool to deal with initial and boundary value differential problems. This numerical method can be useful in any math – based theoretical studies i. e. research in physics, chemistry, engineering and life science.
In the case of one – dimensional linear differential equations the Adobe Flash Player presentation (DEMO hidden in Solver 1D) should be a good start. It presents principles of FEM approach in an ease way. After that pay an attention to some simple examples in the page titled the Linear Differential Equation (LDE). A piece of theoretical information is accompanied by programs written in Octave (MATLAB). If you are not familiar with this programming language yet do not worry. You can take a course in Octave (MATLAB) programming or you can read Octave (MATLAB) documentation and/or help and use tips given therein. Numerical codes are also part of introduction to the time-dependent LDE discussing the Weighted Residual Approach and the Taylor Series Collocation Method.
In the case of two-dimensional linear differential equations look through the article below (hidden in Solver 2D). It gives you the main idea how the metfem2d program works.
Mathematical concept of the finite element method (FEM) in one dimensional case is put forward. From this tutorial one can learn how to solve one-dimensional differential equations using fem approach.
The Adobe Flash Player demo runs very slowly that you can read all pages. However, if it seems to be too slow for you let it end and then start it again and manually navigate between pages.
Software to test: metfem2d. This software is written in Java and solves linear differential equations using finite element method approach. Mathematical concept of finite element method is described below.
Software to test: metfem3d. This software is written in Java and solves linear differential equations using finite element method approach. Mathematical concept of finite element method is described below.