Finite element method for chemical engineering applications

Abstract

The finite element method, or FEM, is one of numerical methods, which is used to solve manyengineering problems efficiently. It provides better alternative thai is suitable for systems with irregular geometry, unusual boundary boundary conditions, or heterogeneous composition. It divides the domain into simply shaped regions, or "element". An approximate solution for partial differential equation (PDE) can be developed for each of these elements. The total solution is then generated by linking together, or "assembling". The PDE will eventully be in form of system of linear algebraic equation, which can be solved by a conventional method like iterative or Gauss elimination. In this work, FEM was applied to a two-dimensional Poisson's equation, which covers many problems in chemical engineering applications. The FEM application program was developed via the Visual Basic programming language, using method of Galerkin weighted residual, and was then tested with four practical problems. The program is accurate, reliable, convenient and effective, and has a very useful graphical interface. The accuracy of numerical solution can be improved by using refined meshing as user alternative.