A physical perspective of the element-based finite volume method and FEM-Galerkin methods within the framework of the space of finite elements

The literature shows an increasing number of works focused on investigating the behaviour of methods that uses concepts of control volumes in the solution of structural problems. In recent years, new approaches using unstructured meshes have been proposed, most of which addressing new applications and, to a lesser extent, the underling physical perspective. This paper presents a unified approach to the element-based finite volume method and FEM-Galerkin within the framework of the finite element space. Numerical examples highlight some accuracy issues associated with the element-based finite volume method developed in this work. Copyright (c) 2014 John Wiley & Sons, Ltd.