**Course Description**

The fundamentals of the most versatile numerical tool in engineering and science, the Finite Element Method (FEM), limitations of applicability of the FEM, introduction to the open world of a class of methods, named as the Mesh-free methods (M-Free) and description of one of such methods would be attempted in this course.

**Course Objectives**

1. Introduce the Finite Element Method from the scratch through solid mechanics applications.

2. Motivate the students to generate an affinity towards assimilating the fundamentals of the FEM before attempting any computer program of which the FEM is a black box.

3. Illustrate the FEM (in 1D and 2D) through certain typical benchmark examples from solid mechanics and numerical procedure for integration, solution of equations (linear, non-linear and eigen value problems).

4. Throw light on the limitations of the applicability of the mesh-based methods and the remedies adopted to overcome the same, in the literature.

5. Introduce the mesh free concept and illustrate the same through one of the integral equation representation mesh-free methods, the Reproducing Kernel Particle Method (RKPM).

**Prerequisites**

1. Exposure to linear solid mechanics (equations of equilibrium, compatibility, boundary conditions, applications, etc.).

2. Exposure to linear algebra (matrices and their operations), calculus and partial differential equations.