Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation

Authors:
Open Access
Publisher website
Google Scholar
Abstract
We present the first a priori error analysis of the hybridizable discontinuous Galerkin methods for the acoustic equation in the time-continuous case. We show that the velocity and the gradient converge with the optimal order of k + 1 k+1 in the L 2 L^2 -norm uniformly in time whenever polynomials of degree k ≥ 0 k \geq 0 are used. Finally, we show how to take advantage of this local postprocessing to obtain an approximation to the original scalar unknown also converging with order k + 2 k+2 for k ≥ 1 k \geq 1 . This puts on firm mathematical ground the numerical results obtained in J. Comput. Phys. 230 (2011), 3695–3718.

This publication has 59 references indexed in Scilit: