Galerkin Variational Method

The Galerkin Variational Method is a mathematical technique used to find approximate solutions to complex problems, such as differential equations. It involves choosing a set of simple functions, called basis functions, to represent the solution. The method then adjusts the combination of these functions to minimize the difference (error) between the approximation and the exact solution, based on a principle called the variational formulation. By projecting the problem onto the span of the basis functions, it transforms a difficult problem into a manageable system of equations, providing an efficient way to approximate solutions in engineering and physics.