Abstract In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator {{V}} V for the wave equation as a minimization problem in L² () L 2 (Σ), where: = (0, T) Σ: = ∂ Ω × (0, T) is the lateral boundary of the space-time domain Q: = (0, T) Q: = Ω × (0, T). For discretization, the minimization problem is restated as a mixed saddle point formulation. Unique solvability is established by combining conforming nested boundary element spaces for the mixed formulation such that the related bilinear form is discrete inf-sup stable. We analyze under which conditions the discrete inf-sup stability is satisfied, and moreover, we show that the mixed formulation provides a simple error indicator, which can be used for adaptivity. We present several numerical experiments showing the applicability of the method to different time-domain boundary integral formulations used in the literature.
Hoonhout et al. (Tue,) studied this question.