Giorgio Giorgiani, David Modesto, Sonia Fernández-Méndez and Antonio Huerta High-order continuous and discontinuous Galerkin methods for wave problems International Journal for Numerical Methods in Fluids 73
The computational efficiency of continuous Galerkin, compact discontinuous Galerkin and hybridizable discontinuous Galerkin is compared for 2D scattering problems in unbounded domains. High-order polynomial approximations out-perform low-order approaches for a wide range of wavelengths, requiring less degrees of freedom, and less runtime, for a given accuracy, for both continuous and discontinuous methods. Continuous Galerkin and hybridizable discontinuous Galerkin exhibit comparable efficiency for high-order approximations, providing similar levels of accuracy for the same computational cost and clearly outperforming compact discontinuous Galerkin.
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