Variational Formulations of Boundary Value Problems
In this chapter we describe and analyze variational methods for second order elliptic boundary value problems as given in Chapter 1. To establish the unique solvability of the associated variational formulations we will use the methods which were given in the previous Chapter 3. The weak formulation of boundary value problem is the basis to introduce finite element methods. Moreover, from these results we can also derive mapping properties of boundary integral operators (cf. Chapter 6) as used in boundary element methods.
KeywordsSaddle Point Variational Problem Bilinear Form Variational Formulation Dirichlet Boundary
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