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

Computers & Mathematics with Applications, vol. 168, pp. 33–38

Abstract

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 θ -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.

Authors 1

1. Douglas R. Q. Pacheco corresponding Aachen Chair for Computational Analysis of Technical Systems (CATS) Chair of Methods for Model‐based Development in Computational Engineering

   RWTH Aachen University · Norwegian University of Science and Technology

   Affiliation as printed

   Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany

   Chair of Methods for Model-based Development in Computational Engineering, RWTH Aachen University, Germany

   Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway