A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part II : Analysis

Francis Collino (1) , Thierry Fouquet (1) , Patrick Joly (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We introduced in [2] a new method for space-time refinement for the 1-D wave equation. This method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme. In this second part, we analyse the accuracy of this scheme in a detailed way by means of a plane wave analysis and numerical experiments that permit us to point out spurious numerical phenomena and explain how to control them.

Francis Collino, Thierry Fouquet, Patrick Joly. A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part II : Analysis. Numerische Mathematik, 2003, 95 (2), pp.223-251. ⟨10.1007/s00211-002-0447-4⟩. ⟨hal-00989023⟩