The wave equation is a basic PDE model central to a plethora of physical and engineering applications, with such applications requiring approximate solutions obtained by numerical schemes. In this talk, I will focus on the space semi-discretization of the wave equation with a finite element method (and assume that time integration is exactly performed). In the context of finite element methods, a posteriori error estimates are a now widely established technique to rigorously control the discretization error, and to drive adaptive processes where the finite element mesh is iteratively refined. However, although a posteriori error estimates are widely available for elliptic and parabolic problems, the literature is much scarcer for hyperbolic problems, including the time-dependent wave equation. In this talk, I will discuss a new a posteriori error estimator that hinges on ideas previously developed for the Helmholtz equation (the time-harmonic version of the wave equation). To the best of my knowledge, this new error estimator is the first to provide both an upper and a lower bound for the error measured in the same norm. I will also briefly quickly discuss preliminary results concerning time discretization, and application to adaptive algorithms.

For further information about the seminar, please visit this webpage.