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High-order conforming finite elements for the Cahn-Hilliard equation: Relative-energy stability and energy defects

arXiv:2606.06719v1 Announce Type: new Abstract: We study a semidiscrete single-field Galerkin approximation of the Cahn-Hilliard equation using high-order conforming finite element spaces. More specifically, globally $C^1$ finite elements with $H^2$-conforming trial spaces, including Argyris, Bell, and Bogner-Fox-Schmit elements, allow a direct discretization of the fourth-order formulation and preserve mass exactly. The main structural result is an exact energy balance for the physical...

arXiv CS 2d ago

Tests suggest Russian satellites can jam GPS on a continental scale

Russian satellites have been identified as the cause of mysterious, seconds-long bursts of GPS interference across Europe—a rare example of human-made GPS interference coming from space. But uncertainty still hangs over whether such interference is intentional and if it could be more powerfully weaponized as GPS jamming with continental reach in the future. The discovery came from an investigation detailed in a June 2 preprint paper by Todd Humphreys and his student Zach Clements at The...

Ars Technica 1d ago