Preface

摘要

Numerical methods to solve partial differential equations (PDE) play a major role in the engineering sciences and lead to effective developments in the technology of modern societies, mainly in the last decades. The acknowledgement of the importance of the numerical methods led to discussions on which is the best "numerical approach" to solve PDE problems. At the earlier stages of the development of numerical methods, finite element methods (FEM) showed some advantages over finite difference methods (FDM), and took the lead as a "general purpose solver" for PDEs. It has been clear, over the years, which idea of the FEM (or in fact, any other method) as the "general purpose solver" is outdated. In fact, it is quite easy to find simple problems where FEM performs poorly as compared with other methods.