Least-squares spectral element method for non-linear hyperbolic differential equations

• DOI: 10.1016/j.cam.2006.03.060
• Publication Date: 2006-12-21T07:25:19Z
• Authors: B. De Maerschalck; M.I. Gerritsma
• Keywords: Least-squares function approximation

AbstractThe least-squares spectral element method has been applied to the one-dimensional inviscid Burgers equation which allows for discontinuous solutions. In order to achieve high order accuracy both in space and in time a space–time formulation has been applied. The Burgers equation has been discretized in three different ways: a non-conservative formulation, a conservative system with two variables and two equations: one first order linear PDE and one linearized algebraic equation, and finally a variant on this conservative formulation applied to a direct minimization with a QR-decomposition at elemental level. For all three formulations an h/p-convergence study has been performed and the results are discussed in this paper.