The posteriori analysis of the spectral element discretization of the wave equation

Abstract

Abstract This work focuses on discretizing a second-order linear wave equation using the implicit Euler scheme for time discretization and the spectral element method for spatial discretization. We prove that optimal adaptivity can be achieved by combining adaptive time steps with adaptive spectral mesh. We introduce two sets of error indicators for time and space, respectively, and derive optimal estimates.

Keywords

• Second order wave equation
• Implicit Euler method
• Spectral element method
• Posteriori analysis
• Error indicators