ABSTRACT
A brief history of the finite element method is given first in this chapter. After that, fundamentals are examined with the example of an elliptical model problem. To do so, Sobolev spaces, the variational formulation, and the RitzGalerkin method are introduced, which leads to an approximate finite element solution of the model problem. Furthermore, the influence of mesh quality on solution accuracy and stability is discussed through the example of an iteratively distorted mesh.
