4 papers
Nonlinear semigroups with unbounded generators under Carleman linearization
Sitanshu Gakkhar, Ala Shayeghi, David C. Del Rey Fernández
We treat the convergence of Carleman linearization of nonlinear evolutionary equations through the approximation theory of strongly continuous semigroups, by Carleman embedding the…
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physi…
SBP-FDEC: Summation-by-Parts Finite Difference Exterior Calculus
Daniel Bach, Andrés M. Rueda-Ramírez, Eric Sonnendrücker +2
We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and…
Fully-discrete provably Lyapunov consistent discretizations for convection-diffusion-reaction PDE systems
Rasha Al Jahdali, David C. Del Rey Fernandez, Lisandro Dalcin +1
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population o…