A new LPS-ROM for incompressible Navier-Stokes is proposed and analyzed with error estimates, tested numerically on 2D unsteady flow past a circular obstacle.
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A fully discrete DG-IMEX pressure-correction scheme for the PNP-NS equations is proposed, with optimal L2 and energy-norm error estimates plus exact discrete mass conservation for both ion species.
Introduces an a posteriori stabilization strategy for POD-ROMs in strongly advection-dominated advection-diffusion-reaction problems, applied to both snapshot generation and new simulations.
A completely discrete DG finite element scheme with first-order time discretization is proposed for the incompressible chemotaxis-Navier-Stokes equations, yielding optimal L2 and H1 error bounds for density, concentration, and velocity plus L2 for pressure.
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A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations
Introduces an a posteriori stabilization strategy for POD-ROMs in strongly advection-dominated advection-diffusion-reaction problems, applied to both snapshot generation and new simulations.