Discretization of the Wave Equation Using Continuous Elements in Time and a Hybridizable Discontinuous Galerkin Method in Space

作者：Griesmaier Roland^*; Monk Peter

来源：Journal of Scientific Computing, 2014, 58(2): 472-498.

DOI：10.1007/s10915-013-9741-9

• Discontinuous Galerkin method
• Hybridization
• Continuous time Galerkin method
• Error analysis
• Wave equation

We provide an error analysis of two methods for time stepping the wave equation. These are based on the Hybridizable Discontinuous Galerkin (HDG) method to discretize in space, and the continuous Galerkin method to discretize in time. Two variants of HDG are proposed: a dissipative method based on the standard numerical flux used for elliptic problems, and a non-dissipative method based on a new choice of the flux involving time derivatives. The analysis of the fully discrete problem is based on simplified arguments using projections rather than explicit interpolants used in previous work. Some numerical results are shown that illuminate the theory.

• 出版日期2014-2