Error Analysis for a Hybridizable Discontinuous Galerkin Method for the Helmholtz Equation

Authors:
Roland Griesmaier;Peter Monk
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, USA 19716;Department of Mathematical Sciences, University of Delaware, Newark, USA 19716
Venue:
Journal of Scientific Computing
Year:
2011

Citing 1
Cited 2

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

SIAM Journal on Numerical Analysis

Error Estimates of the Finite Element Method for Interior Transmission Problems

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

Journal of Scientific Computing

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Abstract

Finite element methods for acoustic wave propagation problems at higher frequency result in very large matrices due to the need to resolve the wave. This problem is made worse by discontinuous Galerkin methods that typically have more degrees of freedom than similar conforming methods. However hybridizable discontinuous Galerkin methods offer an attractive alternative because degrees of freedom in each triangle can be cheaply removed from the global computation and the method reduces to solving only for degrees of freedom on the skeleton of the mesh. In this paper we derive new error estimates for a hybridizable discontinuous Galerkin scheme applied to the Helmholtz equation. We also provide extensive numerical results that probe the optimality of these results. An interesting observation is that, after eliminating the internal element degrees of freedom, the condition number of the condensed hybridized system is seen to be almost independent of the wave number.