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Pressure-robust and quasioptimal Discontinuous Galerkin discretisations of the $p$-Stokes problem
arXiv:2606.09586v1 Announce Type: new Abstract: In the present paper, we propose Local Discontinuous Galerkin (LDG) approximations for a nonlinear system of $p$-Stokes type, having $(p,\delta)$-structure. On the basis of the primal formulation, we prove well-posedness and stability (a priori estimates) of the methods under truly minimal regularity assumptions. We show that the first method possesses a pressure-robust and quasi-optimal error estimate, and discuss its consequences.
Generalizing Multi-Scale Time-Series Modeling with a Single Operator
arXiv:2605.31129v1 Announce Type: new Abstract: Multi-scale modeling has emerged as an effective design principle for time-series forecasting by capturing temporal dynamics at multiple resolutions. As no principled foundation has been established in the literature, we unify existing scaling methods into a scaling operator family, revealing a fundamental limitation of existing approaches: reliance on fixed and discrete scaling. To address this limitation, we propose SiGMA (Single Generalized...