
1
Chapter 1
Introduction
1.1 BACKGROUND
One of the most important advances in the eld of numerical methods was
the development of the nite element method (FEM) in the late 1950s. In
FEM, a continuum is divided into discrete elements that are connected
together by a topological map and usually are called meshes. FEM is a
robust and thoroughly developed method for computational science and
engineering. However, FEM has several shortcomings, for example:
• Difculty in meshing and re-meshing
• Low accuracy, especially for computing stresses
• Difculties when dealing with certain class of problems
− Simulating the dynamic crack growth with arbitrar ...