On the temporal stability of least-squares methods for linear hyperbolic problems

Standard Galerkin methods often perform poorly for problems with low diffusion. In particular for purely convective transport, least -squares (LS) formulations provide a good alternative. While spatial stability is relatively straightforward in a least -squares finite element framework, estimates in time are restricted, in most cases, to one dimension. This article presents temporal stability proofs for the LS formulation of O -schemes, including unconditional stability for the backward Euler and Crank-Nicolson methods in two or three dimensions. The theory includes also the linear advection-reaction equation. A series of numerical experiments confirm that the new stability estimates are sharp.