Hybrid High-Order Methods for the Acoustic Wave Equation in the Time Domain

We devise hybrid high-order (HHO) methods for the acoustic wave equation in time domain. first consider second-order formulation time. Using Newmark scheme temporal discretization, we show that resulting HHO-Newmark is energy-conservative, and this also amenable to static condensation at each step. then of as a first-order system together with singly-diagonally implicit explicit Runge-Kutta (SDIRK ERK) schemes. HHO-SDIRK schemes are For HHO-ERK schemes, use mixed-order formulation, where polynomial degree cell unknowns one order higher than face unknowns, key benefit from structure scheme. Numerical results on test cases analytical solutions can deliver optimal convergence rates smooth $$\mathcal{O}(h^{k+1})$$ $$H^1$$ -norm $$\mathcal{O}(h^{k+2})$$ $$L^2$$ -norm. Moreover, propagation heterogeneous media indicate benefits using methods.