Auth: Vinay Prashanth Subbiah (Tutor: Prof. S. Mittal)
Book Summary: This technical presentation provides a foundational, step-by-step introduction to the Finite Element Method (FEM), focusing specifically on applying variational techniques to solve the classical Laplace and Poisson equations. Originating from the Indian Institute of Technology, Madras, the text bridges pure mathematics and computational physics.
The work outlines how to convert strong-form partial differential equations (PDEs)—which govern steady-state physical phenomena like heat conduction, electrostatics, and potential flow—into their weak or variational formulations (such as the principle of minimum potential energy or the Galerkin method). It details the mathematical prerequisites, the selection of trial and test functions, and the boundary conditions required to set up solvable discrete algebraic equations over finite subdomains.
