Well-posedness of first-order acoustic wave equations and space-time finite element approximation
Abstract
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L2. The results rely on well-posedness and stability of the weak and ultraweak formulation of the second-order wave equation. As an application we define and analyze a space-time least-squares finite element method for solving the wave equation. Some numerical examples for one- and two- dimensional spatial domains are presented.
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