Fully discrete DG methods for the wave equation exhibit a space-time dispersion trapping effect that drives exp(h^{-(1-ε)}) blow-up in observability constants, which spectral filtering can restore uniformly, with higher orders preserving more physical frequencies and lowering filtering cost.
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2026 2verdicts
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A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.
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Fully Discrete High-Order DG Schemes for Waves: Dispersion and Observability
Fully discrete DG methods for the wave equation exhibit a space-time dispersion trapping effect that drives exp(h^{-(1-ε)}) blow-up in observability constants, which spectral filtering can restore uniformly, with higher orders preserving more physical frequencies and lowering filtering cost.
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Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.