Solution of differential equations using the finite element method

Abstract

The finite element method (FEM) is a useful tool to solve boundary value problems of interest in applied geophysics. 1-D finite element spaces are first defined and analyzed. The concept of continuous and discrete weak solutions is introduced and a priori error estimates are stated. The FEM is used to solve wave propagation problems and to characterize fine layered media in the 1-D case. Next, 2-D and 3-D conforming and non-conforming finite element spaces and defined over partitions of a bounded domain into triangular or rectangular elements in 2-D and tetrahedral or 3-rectangular elements in 3-D. These finite element spaces are used in the following Chapters to represent solid or fluid vector displacements in the boundary value problems to be formulated and solved using the FEM.