78 citations · 152 across the 12 of their papers we have counts for
Showing math.APShow all
3 papers · 1 filter
math.AP2020
Rigorous FEM for 1D Burgers equation
Piotr Kalita, Piotr Zgliczyński
We propose a method to integrate dissipative PDEs rigorously forward in time with the use of Finite Element Method (FEM). The technique is based on the Galerkin projection on the F…
math.AP2016★ 2 cited
Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces
Jacek Cyranka, Piotr B Mucha, Edriss S Titi +1
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time extern…
math.AP2015
Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing
Aleksander Czechowski, Piotr Zgliczyński
We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of…