FEMSTER: An object-oriented class library of high-order discrete differential forms
ACM Transactions on Mathematical Software (TOMS)
Journal of Scientific Computing
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Parallel hp-Finite Element Simulations of 3D Resistivity Logging Instruments
Proceedings of the 2006 conference on Leading the Web in Concurrent Engineering: Next Generation Concurrent Engineering
A multiscale hp-FEM for 2D photonic crystal bands
Journal of Computational Physics
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Insights from von Neumann analysis of high-order flux reconstruction schemes
Journal of Computational Physics
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version
SIAM Journal on Numerical Analysis
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
SIAM Journal on Numerical Analysis
An optimally blended finite-spectral element scheme with minimal dispersion for Maxwell equations
Journal of Computational Physics
Overlapping solution finite element method - Higher order approximation and implementation
Applied Numerical Mathematics
Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number
Journal of Computational Physics
Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods
Journal of Scientific Computing
General DG-Methods for Highly Indefinite Helmholtz Problems
Journal of Scientific Computing
An analysis of discretizations of the Helmholtz equation in L2 and in negative norms
Computers & Mathematics with Applications
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The dispersive properties of high order finite element schemes are analyzed in the setting of the Helmholtz equation, and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order. It is shown that the numerical dispersion displays three different types of behavior, depending on the size of the order of the method relative to the mesh-size and the wave number. Quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes. All estimates are fully explicit and are shown to be sharp. Limits are obtained, where transitions between the different regimes occur, and used to provide guidelines for the selection of the mesh-size and the polynomial order in terms of the wave number so that the dispersion error is controlled.