Solution of Dirichlet Pure Diffusion Problem Using Galerkin Method

Abstract

Dirichlet pure diffusion problem refers to physical problem which only includes diffusion effect on the transport of variable within a continuum. It can be solved by central differencing finite volume method with good accuracy, provided that sufficient grids are prescribed. However, the solution using finite volume method may have high computational cost when the large number of grids takes place. Hence, in this study, Galerkin method is used as an alternative to solve the Dirichlet pure diffusion problem. Galerkin method is a numerical approach used to obtain numerical approximation by converting a continuous operator problem such as differential equation to a discrete problem. However Galerkin method is proven not to be a good tool for solution of this higher order partial differential equation physical problems due to its low accuracy, high complexity and unsatisfactory accessibility.