This monograph is a component of Indian Institute of Science collaboration (IISc) Research Monographs Series. The development of most of numerical methods was split between those based on finite difference approaches and those based on finite element approaches; likewise, applications of such numerical methods were split between solids and fluids. The control volume finite method was constructed later, starting with the pioneering work of A. M. Winslow [J. Comput. Phys. 1, 149–172 (1966; Zbl 0254.65069)]. This method is viewed as bridging between finite difference method (FDM) and finite element method (FEM), with the ability to adopt and adapt the advantages of these methods. The FDM is restricted to a grid that is constrained to coincide with the coordinate directions. The FEM has no such restriction and can operate on an arbitrary mesh optimized to problem domains. The control volume finite element method (CVFEM) is based on finite element technologies and uses control volumes of a grid of finite elements to arrive at discrete equations based on the consideration of physical integral principles.
The central aim of this monograph is to introduce basic and essential ingredients of CVFEM, in order to provide the researchers with the tools that allow for more general applications of CVFEM. A notable feature of CVFEM is a relative ease by which CVFEM can be applied to both solid and fluid problems. This monograph develops the basic constructions of CVFEM to solve fundamental problems for both solids and fluids. The solutions of some classical problems are constructed, which show high accuracy and efficiency of CVFEM in a wide range of applications.