A comparison of partition of unity finite element method and finite volume technique for solving 1-D heat conduction problems

Abstract

The scope of this research concerns with the numerical methods used for solving one-dimensional partial differential equations. It is motivated by the need for efficient numerical methods to deal with partial differential equations that are difficult to solve using analytical approaches. Among those numerical methods, the Finite Difference Method (FDM) is the simplest method, and the Finite Volume Method (FVM) is generally expected to provide better conservation properties. Also, the Partition of Unity Finite Element Method (PUFEM) has been identified as an extremely powerful new numerical method which deals with overlapping subdomains. In this study, we examined the PUFEM and FVM to see whether they produced equivalent numerical solutions. We considered two problems namely, a steady-state heat conduction problem and an unsteady state heat conduction problem when Dirichlet boundary conditions are given, for this study.