Finite Element Analysis Session 07 Weighted Residual Methods

The Finite Element Method (FEM) is an analysis technique that is applicable to a broad range of problems. With this technique systems are described by mathematical equations. While these equations can be derived for simple objects, finding a solution that describes a complete complex structure is generally not practical. FEM addresses this difficulty by dividing a complex system into smaller objects so that the solution for each object can be represented by an equation much simpler than that required by the entire system. A weighted residual is simply the integral over the domain of the residual multiplied by a weight function, . ... A common approach, known as the Galerkin method, is to set the weight functions equal to the functions used to approximate the solution.