ABSTRACT
In this chapter, we study a representative class of indefinite problems related to wave propagation. As a model example, we will use the problem of a vibrating elastic bar, discussed in Subsection 1.6.3. We begin with a short presentation on the well-posedness of noncoercive problems, and a convergence analysis for such problems. In particular, we discuss the asymptotic optimality of the Galerkin method and its relation to the dispersion error. Finally, we apply the automatic hp adaptivity to solve the model problem.
